Mathematical model of the linear elasticity problem for capillary-porous materials with fractal structure is constructed. The basic physical and geometric relationships of the stress-strain state of the considered material are obtained. Integro-differentiation apparatus of fractional order to account the fractal structure of the material in the ratios of linear elasticity was used. A variational formulation of the linear elasticity problem for capillary-porous materials with fractal structure is obtained. A method for getting an approximate solution for the considered problem is proposed. For partial cases the results obtained are analyzed.