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A semi-analytical approach is presented to obtain the thermomechanical fields of a medium that contains elliptical inclusion(s).Permissible functions that satisfy the homogeneous boundary condition and continuity conditions across the interface between the inclusion and the matrix are derived analytically which can be used to obtain the eigenfunctions for the medium that represent the elliptical geometries.The mechanical and thermal fields can be expressed by a combination of the eigenfunctions.The method presented is favorably compared with numerical results.