The problems of the theories of elasticity and thermoelasticity, Integral and Differential Equations of Mathematical Physics, Boundary Value and Initial Boundary Value Problems of the mechanics of solid deformations are studied, In particular, an explicit solutions of the basic boundary value problems of the theories of elasticity and thermoelasticity are constructed taking into account different physical fields (microtemperatures, porosity, diffusion, voids). The obtained solution of the considered problem is represented as absolutely and uniformly convergent series.