Exhibit 99.1

Contacts:
Third Wave Technologies                     Vida Communication
Rod Hise                                    Stephanie Diaz (investors)
(608) 663-4010                              (415) 885-2298

                                            Tim Brons (media)
                                            (646) 319-8981

For Immediate Release

               THIRD WAVE REPORTS FIRST-QUARTER FINANCIAL RESULTS
                Company's fundamentals and strategy remain strong

      MADISON, Wis., May 5, 2005--Third Wave Technologies Inc. (Nasdaq: TWTI)
today reported financial results for the first quarter ended March 31, 2005.

      Third Wave reported total revenues of $7.1 million and a net loss of $4.4
million, or ($0.11) per diluted share, for the quarter ended March 31, 2005,
compared to total revenues of $15.3 million and net income of $2.8 million, or
$0.07 per diluted share, for the same period of 2004.

      The company reported clinical molecular diagnostic revenue of $3.1 million
for the first quarter of 2005. U.S. clinical revenue increased 15% over the
prior-year period. The sequential quarter-to-quarter decline in clinical revenue
was due to the timing of large orders with certain labs in both the United
States and Japan that totaled more than $1.0 million in revenue, a delay by the
company's supplier of its new CFTR microfluidic format, and slower than
anticipated customer adoption of the company's HCV ASRs due in large part to
performance issues with Roche Diagnostics' MagnaPure sample preparation
instrument. Both delays were temporary and the company believes each has been
resolved.

      Third Wave reported gross margins of 72% for the quarter ended March 31,
2005, further demonstrating the power of the company's new operating model. The
company's gross margin remained above 70% for the fifth consecutive quarter,
despite a drop in revenue in this quarter. Total operating expenses were $11.6
million for the first quarter of 2005, compared to $11.8 million for the same
period of 2004. General and administrative costs were higher due to patent
litigation the company is prosecuting and consulting fees related to a study of
the company's pipeline value and distribution options for its expanding
molecular diagnostic product menu and pipeline.

      The company ended the first quarter of 2005 with cash, cash equivalents
and short-term investments of $64.5 million.



      "Customer acceptance and support of Third Wave's molecular diagnostic
products are growing and we are beginning to see the fruits of our investments
in research and development, and sales distribution. This important progress is
not apparent in a quarterly financial update, but we can see our traction in the
marketplace," said John J. Puisis, president and chief executive officer of
Third Wave. "The lower revenue for the quarter was the result of less research
revenue, a temporary delay by the supplier of our new microfluidic format, and
performance issues with Roche's MagnaPure instrument that put a short-term halt
to the rollout of our HCV genotyping analyte-specific reagents.

      "As expected, our research revenue will continue to be lower than it has
been historically," Mr. Puisis said. "We believe the temporary delays that
impacted our molecular diagnostic revenue in the first quarter have been
remedied."

Current Product Review

Genetics: Factor V Leiden, Factor II (prothombin) and others

      Third Wave's menu of Invader analyte-specific reagents (ASRs) for Factor V
Leiden, Factor II (prothrombin) and others generated $2.1 million in the first
quarter of 2005, compared to $1.8 million in the same period of 2004 and $2.4
million in the prior quarter. The company has secured three new accounts for
this menu of ASRs in 2005 and remains on track to increase its market
penetration by a total of approximately 15 accounts during the year. The total
number of customers purchasing these ASRs is approximately 120. This category is
expected to continue to grow and revenue should reach at least $10.0 million in
2005. The company also continues its progress towards obtaining FDA clearance of
its Factor V Leiden and Factor II (prothrombin) products later this year.

Infectious Disease: HCV

      Third Wave's Invader HCV ASRs, which were released late in the second
quarter of 2004, generated nominal revenue during the first quarter ended March
31, 2005. As described above, customer adoption and validation of the company's
HCV ASRs has been slowed in large part by external factors. Roche Diagnostics,
the market leader in HCV viral load testing, experienced product performance
issues with its MagnaPure sample preparation instrument while moving its
customer base to a new generation of HCV viral load reagents. The by-product of
an HCV viral load test is used in conjunction with Invader HCV genotyping ASRs.
As a result, Third Wave's efforts to convert customers to its HCV genotyping
ASRs were slowed. Customers have indicated that Roche has fixed its
product-related issues.



         Customer feedback and sentiment about the company's HCV ASRs remain
very positive and the company anticipates that orders for its HCV genotyping
ASRs will accelerate through 2005. The company has increased its HCV market
penetration by four accounts during the first quarter and anticipates that
approximately 25 other customers have begun or will begin validating its HCV
ASRs during the second and third quarters of 2005. The company remains confident
about the market potential of its HCV genotyping ASRs and expects to secure
40-50 customers in total during 2005 with an estimated annual run-rate of
$7.0-8.0 million. Depending on the timing of customer validations, the company
anticipates 2005 revenue of at least $5.0 million.

      Third Wave also expects that data from independent studies by
well-respected thought-leaders of its HCV ASRs will be presented at the annual
Clinical Virology Symposium being held May 8-11, in Clearwater Beach, Fla.

Genetics: CFTR

      Third Wave's Invader ASRs that enable laboratories to develop tests for
cystic fibrosis gene detection (CFTR) generated $0.5 million in the quarter
ended March 31, 2005, compared to $0.5 million in the same period of 2004 and
$0.7 million in the prior quarter. The company's first-quarter revenue from CFTR
ASRs does not include any revenue contribution from its new CFTR InPlex ASRs.
The company experienced delays by its microfluidic-format supplier, but believes
these delays have been remedied. These delays pushed back the release of the
CFTR InPlex ASRs by several months. The company's new CFTR ASRs were previewed
to customers at the annual meeting of the American College of Medical Genetics
in March. Third Wave has added two new accounts with its traditional CFTR ASRs.
The company anticipates that it will secure 20-30 additional accounts and that
total CFTR ASR revenues, including those from the InPlex format, will reach at
least $6.0 million in 2005.

Oncology: HPV

      Third Wave is continuing to rollout its ASRs for use by laboratories to
develop tests for HPV. An independent study regarding its HPV ASRs was presented
this week at the International Papilloma Virus Conference in Vancouver and is
expected to be presented at the Clearwater Clinical Virology Symposium. The
company will not estimate HPV market penetration or revenue until further
customer feedback is obtained.



Molecular Diagnostic Pipeline Update

      Third Wave remains on track to meet the 2005 product release milestones it
announced last November, including:

o     The combination of the performance and flexibility of the Invader(R)
      chemistry with the sensitivity of a rudimentary form of PCR whose patents
      expired at the end of March. The coupling of these two fundamental
      chemistries will bring to customers the best of both. Third Wave believes
      this will provide the most robust chemistry combination for customers,
      enabling them to perform complicated molecular testing more simply and
      quickly. The company plans to leverage this new, proprietary chemistry
      aggressively, with an initial focus on the most significant molecular
      market: infectious disease.

o     The release of ASRs for laboratories to develop tests for the human herpes
      virus family, including Herpes simplex viruses 1 and 2, cytomegalovirus,
      Varicella-Zoster virus, and Epstein-Barr virus. The company continues to
      expect that it will release these products during the second half of 2005.

o     The company continues to develop, test and enhance products that include
      HCV detection and viral load, and HIV detection. It will announce more
      specific plans for these valuable product opportunities during the second
      half of 2005.

o     The company will continue to develop new products in the emerging field of
      pharmacogenetics, focusing on genetic markers used to limit the risk to
      patients of adverse reactions to certain drug therapies. The company plans
      to secure FDA clearance in late summer or early fall of a novel test that
      can be used to identify patients at increased risk for adverse drug
      reactions to a major drug used to treat colorectal cancer.

o     Third Wave is currently collaborating with LabCorp on a study using the
      Invader chemistry in the field of cytogenetics. This initial study
      leverages the company's aneuploidy ASRs and will provide insight about the
      company's potential to rival traditional cytogenetics techniques in this
      growing market.

o     The company plans to announce additions to its molecular diagnostic
      product pipeline during the summer of 2005. The company also plans to
      provide further details about markets outside of the United States, as
      well as other opportunities to leverage the Invader chemistry.



2005 Guidance Update

         As the company has stated consistently, it is difficult to provide
quarter-to-quarter clinical revenue guidance, given the infancy of Third Wave's
presence in clinical molecular diagnostics, the number of new products and
variability in the time required for laboratories to review and validate new
tests. The company reiterates its previously issued guidance of $23.0-26.0
million for full-year 2005 clinical molecular diagnostic revenue based on
current customer feedback. The company continues to anticipate growth in its
coagulation-related business and increasing traction from its newer products.

         As the company indicated in past announcements, it expects a
significant decline in research revenue in 2005, particularly in the second
quarter, as the company transitions to next-generation projects with key
researchers. After additional discussions with key research customers, the
company anticipates that its research revenue for full-year 2005 will be at the
low end of its previously issued guidance range of $10.0-15.0 million.

         "As with any company undertaking a complete makeover and transition,
there are several moving pieces," Mr. Puisis said, "and given the fact that two
years ago, Third Wave had virtually no clinical molecular diagnostic revenue, no
clinical product pipeline, and essentially one customer, we have come a long way
with our transition. We have hired great people throughout the ranks and our
customers are giving us positive feedback on our products and pipeline. We are
better positioned today than ever and are excited by our future prospects.

         "We remain focused on achieving $100 million of clinical molecular
diagnostic revenue in the next three years," Mr. Puisis said. "We also continue
to build and develop new products and capabilities that rival the top three
players. Molecular diagnostics is an emerging, growing and valuable market, and
we are positioning Third Wave very well to capture value."

Conference Call & Webcast

         Company management will host a conference call on Thursday, May 5,
2005, at 10 a.m. EST to discuss first-quarter 2005 results and ongoing corporate
activities. Domestic callers should dial (888) 396-2298 and international
callers should dial (617) 847-8708. The access code for both domestic and
international callers is 33878972. Please dial in five to 10 minutes prior to
the start of conference call. A live webcast and a replay of the conference call
will be available at www.twt.com. The conference call, webcast and replay are
open to all interested parties.



About Third Wave Technologies

         Third Wave Technologies is a leader in the development and marketing of
molecular diagnostics for a variety of DNA and RNA analysis applications,
providing physicians and researchers with superior tools to diagnose and treat
disease. Third Wave's Invader(R) chemistry provides the company's customers with
exceptional performance, scalability and ease of use. The company offers a
number of clinical products based on its Invader(R) chemistry for genetic
testing related to multiple disease areas. For more information about Third Wave
and its products, please visit the company's website at www.twt.com.

All statements in this news release that are not historical are forward-looking
statements within the meaning of the Securities Exchange Act of 1934 as amended.
Such forward-looking statements are subject to factors that could cause actual
results to differ materially for Third Wave from those projected. Those factors
include risks and uncertainties relating to the company's ability to bring new
products to market as anticipated, the current regulatory environment in which
the company sells its products, the market acceptance of those products,
dependence on partners and customers, successful performance under collaborative
and commercial agreements, competition, the strength of the Third Wave
intellectual property, the intellectual property of others and other risk
factors identified in the documents Third Wave has filed, or will file, with the
Securities and Exchange Commission. Copies of the Third Wave filings with the
SEC may be obtained from the SEC Internet site at www.sec.gov. Third Wave
expressly disclaims any obligation or undertaking to release publicly any
updates or revisions to any forward-looking statements contained herein to
reflect any change in Third Wave's expectations with regard thereto or any
change in events, conditions, or circumstances on which any such statements are
based. Third Wave Technologies, Invader and the Third Wave logo are trademarks
of Third Wave Technologies, Inc.

                           --Financial Tables Follow--



                          Third Wave Technologies, Inc
                             Statement of Operations
                  (In thousands, except for per share amounts)
                                   (Unaudited)



                                                                Three Months Ended
                                                                     March 31,
                                                              2005               2004
                                                        ------------------  ----------------
                                                                              
Revenues:
   Product                                                         $6,914           $15,215
   License & royalty                                                   93                41
   Grant                                                              119                20
                                                        ------------------  ----------------
                                                                    7,126            15,276
                                                        ------------------  ----------------

Operating expenses:
   Cost of goods sold
     Product cost of goods sold                                     1,537             3,600
     Intangible and long-term asset amortization                      463               571
                                                        ------------------  ----------------
   Total cost of goods sold                                         2,000             4,171

   Research and development                                         2,465             2,673
   Selling and marketing                                            3,365             2,625
   General and administrative                                       3,779             2,357
                                                        ------------------  ----------------
                                                                    9,609             7,655
                                                        ------------------  ----------------

Total operating expenses                                           11,609            11,826
                                                        ------------------  ----------------

Loss from operations                                               (4,483)            3,450

Other income (expense):
   Interest income                                                    347               127
   Interest expense                                                   (89)              (57)
   Other                                                             (195)             (672)
                                                        ------------------  ----------------
                                                                       63              (602)
                                                        ------------------  ----------------
                                                        ------------------  ----------------

Net income (loss)                                                 ($4,420)           $2,848
                                                        ==================  ================

Net income (loss) per diluted share                                ($0.11)            $0.07

Weighted average diluted shares outstanding                        41,124            41,566





                          Third Wave Technologies, Inc
                                 Balance Sheets
                                   (Unaudited)



                                                            March 31,         December 31,
                                                              2005                2004
                                                        ------------------  ------------------
                                                                                
Assets:
   Cash, cash equivalents, and short-term investments             $64,531             $66,690
   Other current assets                                             6,570               7,281
   Equipment and leasehold improvements, net                        5,610               5,971
   Intangible assets, net of amortization                           3,770               4,146
   Goodwill and indefinite lived intangible assets                  1,497               1,497
   Other assets                                                     2,356               2,483
                                                        ------------------  ------------------
     Total assets                                                 $84,334             $88,068
                                                        ==================  ==================

Liabilities and shareholders' equity
   Accounts payable, accrued expenses and other                   $15,557             $14,781
   liabilities
   Deferred revenue                                                   542                 384
   Debt                                                            10,219              10,168
   Shareholders' equity                                            58,016              62,735
                                                        ------------------  ------------------
     Total liabilities and shareholders' equity                   $84,334             $88,068
                                                        ==================  ==================