The elastic wave propagations in deformed crystals with any symmetry are investigated theoretically. The rotationless acoustical tensor, which specifies the propagation condition, consists of the tensor based on the natural unstressed state and the perturbation term being proportional to the stress. The perturbation theory is applied to nondegenerate and degenerate cases with respect to the quasitransverse wave velocities. The perturbed wave velocities and the polarization directions are formulated by the stress suppressed on the crystals, and then the general formulas for the acoustical birefringence depending on the second‐ and third‐order elastic constants are reduced. The difference of the quasitransverse wave velocities is expressed by the sum of two terms: the difference of these in unstressed crystals due to the intrinsic anisotropy and the perturbation term due to the stress. In the cases of the cubic system and of the isotropic material, the explicit relations are calculated. For the isotropic material, the so‐called stress‐acoustical law holds.