Abstract: To maintain the calculation precision in solving Lord and Shulman (L-S) type generalized thermoelastic problems by means of integral transform technique, the newly developed so-called direct finite element method is adopted to solve the dynamic response of a two-dimensional half-space subjected to a thermal shock, in which the generalized thermoelastic coupling is considered. In the context of Lord and Shulman generalized thermoelastic theory, the results are obtained with high precision by using the direct finite element method. The L-S type generalized thermoelastic coupling governing equations, the general form of virtual displacement principle as well as the corresponding finite element equations are formulated in this paper. The distributions of dimensionless temperature, dimensionless displacement and dimensionless stress are generated and displayed graphically. The distribution of temperature demonstrates clearly the unique characteristic of heat wave front, i.e., a sharp jump of temperature in the position of heat wave front.