The propagation of mechanical and thermal disturbances in a half-space is studied by means of the solution of some transient boundary value problems, according to the coupled thermoelastic theory. The problems considered are those of a half-space under step time variations of strain, temperature, or stress uniformly distributed over the free surface. The coupled solution of Danilovskaya’s problem is thus included. The solution is obtained by the use of Fourier sine transforms, and the behaviors at short and long times, as well as the propagation of discontinuities, are studied.