The aim of this paper is to illustrate the effect of initial stresses on the propagation of plane waves in a general anisotropic elastic medium. Therefore, an analytical analysis supported by numerical tests to calculate the bulk acoustic wave propagation in Aluminum Nitrite (AlN) as piezoelectric hexagonal elastic material has been presented. In addition, the Christoffel’s equation has been solved and the corresponding eigenvalues and eigenvectors have been obtained. Then, an explicit expressions of the waves propagation with three distinct phase velocities in anisotropic piezoelectric material including the effect of the initial stresses have been derived. The three velocities of bulk acoustic waves (BAW) which are called quasi-longitudinal, quasi-shear vertical and quasi-shear horizontal for Aluminum Nitrite are numerically calculated. The numerical examples are considered to illustrate graphically the effect of initial