In the present article, we apply the eigenvalue approach on the twodimension problem of thermoelasticity in the context of the Green- Lindsay theory (G-L) with two relaxation times, coupled theory (CD) and Lord- Shulman theory (L-S) with one relaxation time. The governing equations of the thermoelastic medium with two temperatures are solved for surface wave solutions. The numerical estimates of the quantities of physical interest is obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, twotemperature parameter, rotation, magnetic field, and mechanical force.