Abstract—The present work is aimed at the study the analytical and numerical solutions of thermoelastic problem in a semi-infinite medium in the context of the Green and Naghdi theory of type III. The governing equations are expressed in Laplace transform domain and solved in the domain by analytical method and finite element method. 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.