The propagation of plane waves in fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord-Shulman under hydrostatic initial stress is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of pressure. It is found that the hydrostatic initial stress has a great effect on the distribution of field quantities.