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A finite-element methodology has been presented to solve the one-dimensional couple dynamical thermoelasticity. The spatial variable is discretized by the Galerkin scheme and the central difference scheme. The time variable is discretized by the Galerkin and the backward difference scheme. It was found that the two spatial discretization approaches give close comparison in accuracy when used in conjunction with the backward difference in time. To simulate the wave-like behavior in micro-time scale becomes expensive but there is no technical difficulty. To simulate the macro-time phenomena, the micro-time behavior would disappear. Two test problems are presented to show the micro- and the macro-time behaviors of the thermoelastic slab. The responses to a realistic set of pressure and temperature pulse inputs simulating the interior ballistic type of action are also presented. (Author)