The paper deals with a boundary-value problem of coupled thermoelasticity for a half-layer weakened by a tunnel cavity under mixed boundary conditions. The problem is reduced to a system of four singular integral equations and solved numerically by the method of mechanical quadratures. As a result of numerical experiment dynamical stress concentration is studied for the cavities of different transversal cross-sections and the influence of coupled thermoelastic fields on the character of wave processes in the body is revealed.