Modified model for liquid filtration in elastic fracture-porous material is proposed. Filtration area may be divided into zones with enclosed and open fractures. Pressure and flow parity conditions by units are realized at interzone boundaries; pressure in fracture is equal to critical value and flow is equal to zero. Gas filtration is considered within the frame of this model in the case, when material is under conditions of all-out compression with σ tension. Material filtration-capacity characteristics are nonlinearily dependent on the system tension state. Strong fracture deformation up to their closing is permissible for this method in contrast to known concepts and corresponds to experimental observations. System of equations is obtained; problem related to start-up of gallery with constant driving pressure is solved for illustration purposes.