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In this paper, transfinite element method is used to analyze the two dimensional thermoelasticity problems. A comparison is made between the thermoelastic analysis results of the classical theory and theories with one or two relaxation times (i.e. L-S and G-L theories), for the half space problem. Governing equations are transformed to Laplace domain and then, node variables are calculated by the finite element method. Results are transformed to physical domain by the Laplace inverse transform. Finally, results of the three theories are compared and discussed. The obtained results reveal that the tensional stresses predicted by the classical theory for points located before the stress wavefront are higher whereas the compressive stresses predicted by L-S and G-L theories are higher for points located after the stress wavefront. Furthermore, the temperature predicted by the modern theories is higher than that of by the classical theory at the wavefornt.