The boundary integral equationmethod (BIEM) is one of the most effective numerical methods in engineering analysis. The great advantage of the BIEMis the reduction of dimensions in the formulation for solution of boundary value problems since the unknowns are localized on the boundary instead of the whole analyzed domain. It should be stressed that the dimensional reduction is achieved only in problems when the fundamental solutions of the governing equations are available. Recall that the fundamental solutions are known only in linear theory of thermoelasticity. The temperature and displacement fields (the primary fields) are represented in terms of boundary integrals of relevant boundary densities (temperature, heat flux, displacements, and tractions) and domain integrals of known body sources. The integral representations of the derivatives of the primary fields are expressed in terms of the same boundary densities as in the case of the primary fields.