In the present work we show that in drying of colloidal capillary-porous materials the processes of heat and mass transfer are usually accompanied by the processes of deformation and development of stresses. Application of the Euler approach, which is connected only with the account of small deformations, to description of the occurring processes is erroneous. The stressed-strained state should be described on the basis of the Lagrange approach with account for large displacements and deformations of material. In this connection, we present a physical-mathematical model of the process of drying colloidal capillary-porous materials in curvilinear coordinates in the tensor form. A variational formulation of the problem and its solution by the method of finite elements are presented. The results of calculations and regularities obtained on their bases are given. Special attention is paid to the fact that the developed model and calculation techniques can form a theoretical basis for designing devices of experimental determination of stresses in materials. (C) 2015 Elsevier Ltd. All rights reserved.