The form of a four-rank tensor with the particular intrinsic symmetry for a variety of crystal symmetry is given by the use of the group theory method.

The exact rotational correction of the scattering tensor related to general acoustic modes and pure modes in the higher symmetry directions, for different crystal systems, is presented.

The general form of the third-order nonlinear elastic coefficient tensor having the symmetry of the group so (2) was derived with the help of group theoretical methods.