EXHIBIT 23.4 CONSENT OF INDEPENDENT ACCOUNTANTS We hereby consent to the use in this Registration Statement of First Financial Bankshares, Inc. on Form S-4, of which this Exhibit 23.4 is a part, of our report, dated January 16, 1998, relating to the audited financial statements of Cleburne State Bank as of December 31, 1996 and 1997 and for the three years ended December 31, 1997 appearing in the Prospectus, which is part of this Registration Statement. We also consent to the reference to our Firm under the captions "Experts" and "Selected Financial Data" in the Prospectus. /s/ Rylander, Clay & Opitz, L.L.P. ---------------------------------- RYLANDER, CLAY & OPITZ, L.L.P. Fort Worth, Texas October 1, 1998