Sinha and Sinha (J. Phys. Earth, 22, 237-244, 1974) studied a problem on the reflection of thermoelastic waves at a stress free thermally insulated solid half-space in context of the Lord and Shulman theory of generalized thermoelastcity. He showed the existence of three plane waves (two longitudinal waves and a shear wave) in a homogeneous, linear and isotropic thermoelastic medium. He also obtained the reflection coefficients of reflected waves theoretically and numerically for the incident plane waves. Due to the engineering applications, a problem on the reflection of thermoelastic waves at a non-free boundary surface is considered in this paper. The reflection coefficients of various reflected waves are obtained by considering the new boundary conditions at non-free surface. For a particular material representing the half-space, the reflection coefficients are also computed numerically and are shown graphically against the angle of incidence for different values of boundary parameters.