In this paper we investigated the propagation of SV-waves under effect of the magnetic field, initial stress and two thermal relaxation times. The problem of reflection and transmission of thermoelastic waves at a solid-liquid interface in presence of initial stress and magnetic field has been investigated subjected to certain boundary conditions. The appropriate expressions to find the amplitudes ratios for the incident wave (SV-waves) have been obtained. The reflection and transmitted coefficients for the incident SV-waves are computed numerically, considering the initial stress, relaxation times, and magnetic field effect and presented graphically. The results indicate that the effects of magnetic field, initial stress and two thermal relaxation times are very pronounced.