The problem of propagation of plane WAVE including body and surface WAVEs propagating in a TRANSVERSEly isotropic half-space with a depth-wise axis of material symmetry is investigated in details. Using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations for potential functions. In this paper, the secular equations for determination of body and surface WAVE velocities are derived in terms of both elasticity coefficients and the direction of propagation. In particular, the longitudinal, TRANSVERSE and Rayleigh WAVE velocities are determined in explicit forms. It is also shown that in TRANSVERSEly isotropic materials, a Rayleigh WAVE may propagate in different manner from that of isotropic materials. Some numerical results for synthetic TRANSVERSEly isotropic materials are also illustrated to show the behavior of WAVE motion due to anisotropic nature of the problem.