We propose a phenomenological model of isotropic behavior of composite material with elastomer matrix filled by particles of inert filler. The typical particularities of this type of material are as follows: dependence of the mechanical properties on temperature, nonlinearity of the curve of volumetric compression-extension and its dependence on shear strains, and softening of the material under repeated loading. The model takes into account the structural changes caused by delamination of the matrix and by appearing of pores at the filler boundaries. We propose a variational formulation of step-by-step solution of boundary-value problems. We analyze stress-strain state of a long circular cylinder with elastic steel shell subjected to nonstationary thermal and force loading. The behavior of the cylinder is analyzed for a set of particular variants of the material.