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Two problems of statistical thermoelasticity are considered for an isotropic medium with spherical inhomogeneity. It is assumed that a medium with an inclusion is subjected to piecewise-uniform heating or the action of a homogeneous heat flux. As accurate solutions of the problems are constructed for various types of thermal and mechanical action at the phase interface.

This article examines a problem of static thermoelasticity for an isotropic medium with an ellipsoidal cavity. The orientation of the cavity relative to the heat flow is assumed to be arbitrary. The solution of the problem is constructed in closed form and is expressed through incomplete elliptic integrals of the first and second kinds. In cases when the ellipsoid degenerates into a spheroid or sphere, the stress-strain state can be written in elementary functions of the ellipsoidal coordinate.