In the present work, the electro-elastic effect has been considered for all Curie and point groups of crystal symmetry, except for the triclinic system, when an electric field is applied along the principal crystallographic directions. Relations for the change in acoustic wave velocities under the electric field are derived. It has been shown that, in many cases, the electro-elastic effect behaves similarly to the Pockels effect in optics. The rotation of the eigen vectors of the optical-frequency impermeability tensor caused by the linear electro-optic effect is analogous to the rotation of the eigen vectors of the Christoffel tensor in acoustics. In some symmetry point groups, the application of an electric field necessitates rewriting the elastic stiffness tensor in the rotated coordinate system. It has been found that if the non-orthogonality is induced by the electric field, the dependence of the respective acoustic wave velocities on the electric field is quadratic; otherwise, it is linear. By applying an electric field, one can control the angle of non-orthogonality. The angle of non-orthogonality can be induced by an electric field in all high-symmetry groups, including Curie groups and groups of cubic, middle, and orthorhombic systems, whenever the application of the electric field results in an abrupt lowering of symmetry, at least to the monoclinic system. In this case, the velocities of the AWs that acquire non-orthogonality depend quadratically on the electric field. In cases where the angle of non-orthogonality increases under the electric field, the acoustic wave velocities contain both linear and quadratic terms in the electric field strength.