In the present work, the investigating of the disturbances in a homogeneous, transversely isotropic elastic medium with generalized thermoelastic theory has been concerned. The formulation is applied to generalized thermoelasticity based on three different theories. Laplace and Fourier transforms are used to solve the problem analytically. The essential equations have been written as a vector-matrix differential equation in the Laplace transform domain, then solved by an eigenvalue approach. The inverses of Fourier transforms are obtained analytically. The result is used to solve a specific two-dimensional problem. The technique is illustrated by means of several numerical experiments performed. The results were verified numerically and are plotted.