Effective elastic coefficients for wave propagation obeying all of the classical symmetry relations β ijkm =β kmij =β jikm =β ijmk = … can be defined for crystals of any symmetry under positive or negative hydrostaticpressure. For other states of stress, the full symmetry is lost, even in isotropic materials. The loss of the full symmetry commonly expected of elastic coefficients has a simple physical interpretation the case of uniaxial stress in an isotropic medium. A transverse wave propagates faster in the direction of tension than in the perpendicular direction because tension increases the restoring force for displacements associated with the former wave, just as in a stretched string. The difference in ρV 2 for the two waves equals the tensile stress. Hence, the corresponding effective elastic coefficients, which would be equal under the classical symmetry, also differ by this same amount. In this paper, we define effective elastic coefficients and express them in terms of the stress, the deformation resulting from the stress, and the thermodynamic elastic coefficients, the latter being defined in terms of derivatives of the internal energy with respect to the Lagrangian strain components. When expressed in terms of effective elastic coefficients, the formulas for wave‐propagation velocities in hydrostatically compressed crystals take the same form at any pressure. The quantities usually cited in the ultrasonics literature as pressure derivatives of elastic coefficients are derivatives of the effective coefficients rather than the thermodynamic coefficients. We also define “wave‐propagation coefficients,” which are more convenient than the effective elastic coefficients for discussing wave propagation, especially under nonhydrostatic states of stress. These fall naturally into a 6×6 array that is symmetric under hydrostaticpressure but not in general. In general, 26 of the coefficients are independent.