Abstract: In order to avoid the accuracy loss encountered in the process of numerical inversion in an integral transformation method adopted to solve generalized thermoelastic coupled problems in the context of Lord-Shulman (L-S) theory, the finite element method is used to solve a L-S type generalized thermoelastic coupled dynamic problem of a thin slim strip. The results show that the finite element method is very valid to obtain high calculation accuracy for L-S type generalized one-dimensional themoelastic coupled problem subjected to a thermal shock. The L-S type generalized thermoelastic coupled 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 displayed graphically. From the distribution of temperate, the unique characteristic of heat wave can be observed clearly in the location of heat wave front where a sharp change of temperature gradient occurs.