The filtration of a fluid with an initial gradient in an elastically-compressed cracked porous medium are considered. The effective characteristics of the medium are strongly dependent on the stressed state and the fluid pressure in cracks. Till the cracks are entirely closed, the process is described by a nonlinear system of equations. The asymptotics are given for the steady-state and the non-steady-state cases. A comparison is drawn between nonlinear, linear, and purely cracked media. The conclusions obtained are illustrated by numerical calculations.