A general finite-element model is proposed to deal with dynamic transient response in a square cylinder with an elliptical hole by generalized coupled thermoelastic theory, especially for a long transient period. The method consists of formulating and solving the problem in the Laplace transform domain by the finite-element method and then numerically inverting the transformed solution to obtain the time-domain response. Therefore, the transient solutions at any time can be evaluated directly. Some numerical results, which demonstrate the accuracy, efficiency, and versatility of the proposed method, are presented. Moreover, the effects of the thermoelastic coupling term, inertia term, and relaxation times on solutions are investigated and discussed.