A new model of filtration flows in deformable fractured porous materials taking into account a nonlinear behaviour of the system is elaborated. A well-known nonlinearity of natural fractured oil and gas reservoirs is ignored by using former approaches as a rule. Investigation of basic problem of bringing well into production demonstrates a perspectiveness of the new model as compared with other methods. Besides that a number of principally important results has been obtained. The model is the only one known in literature, which allows correctly to formulate and analyse a new problem of a motion of the fract75re closing front. The existence of a bottom-hole pressure change law optimal for producing of oil or gas volume is established. Obtained results are shown to agree with experimental data.