Summary: Green and Naghdi theory of thermoelasticity is employed to study the reflection and refraction at an interface between two thermoelastic solid half-spaces under hydrostatic initial stress. The amplitude ratios of the reflected and refracted waves are obtained for the incident plane waves. Numerical computations are carried out for a particular example of the model. The effect of hydrostatic initial stress is observed on the amplitude ratios of reflected and refracted waves.