The present investigation is to study the surface wave propagation at imperfect boundary between an isotropic thermoelastic without energy dissipation half-space and an isotropic elastic layer of finite thickness. The penetration depth of longitudinal, transverse, and thermal waves has been obtained. The secular equation for surface waves in compact form is derived after developing the mathematical model. The components of temperature distribution, normal and tangential stress are computed at the interface and presented graphically. The effect of stiffness is shown on the resulting amplitudes and the effect of thermal is shown on the penetration depth of various waves. A particular case of interest is also deduced. Some special cases of interest are also deduced from the present investigation.