Analytical and numerical solutions are two basic tools in the study of thermoelastic interactions problems in anisotropic media. This paper is devoted to a study of the thermoelastic interactions in a semi-infinite medium in the context of the theory of generalized thermoelasticity with one relaxation time (Lord and Shulman's theory). The governing equations are expressed in Laplace transform domain and solved in the domain by analytical method and finite element method. The finite element method is used to obtain approximate solutions which are then compared with analytical solutions. The solutions of the problem in the physical domain are obtained by using a numerical method for the inversion of the Laplace transforms based on Stehfest's method. Numerical results for the temperature distribution, displacement and thermal stress are represented graphically. The accuracy of the finite element formulation was …