The governing equations of coupled thermoelasticity are investigated with the aim of obtaining solutions by means of a perturbation series in the coupling parameter. The perturbation technique is applied to the equations and a simpler set of perturbation equations is obtained. The convergence of the series solution is established, and it is shown that the result is a form of the exact solution to the governing equation for a suitable range of values of the coupling parameter. Numerical results are obtained for a typical problem using only the first two terms of the series solution. A second perturbation technique, well suited to the thermoelasticity problem and based on the method of Krylov and Bogoliuboff, also is presented in this paper. The technique is applied to two problems and the results are compared with the exact solutions.

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