We present resonant ultrasound spectroscopy measurements of the complete elastic moduli of La2-xSrxCuO4 (x=0.00 and 0.14). The x dependence of both the absolute values of the moduli in the tetragonal phase and the temperature dependences of the moduli near the structural phase transition is weak. In both materials c44 and 1/2 (c11-c12) are unaffected by the transition, c33 shows a steplike drop broadened by fluctuations, and c11 and c66 decrease as 1/(T-TSPT) for T>TSPT (where TSPT is the structural phase transition temperature). We also present measurements of the anisotropic thermal expansion coefficients in La1.86Sr0.14CuO4 using a high-resolution capacitance dilatometer. These data when taken together raise serious questions about the standard interpretation of the structural phase transition in La2-xSrxCuO4. © 1994 The American Physical Society.