Subsidence of the surface during the oil and gas production is usually associated with consolidation of reservoir as result of decreasing of pore pressure. However, sometimes it is difficult to explain as in the case of the Ekofisk oil deposit when the local subsidence reach more than 10 meters and which is impossible to stop with help of water injection at the layer. It is shown that this phenomenon may be related with the displacements along the faults that cross the reservoir. The numerical analysis of the action of movements along faults for Ekofisk deposits and oil and gas Russkoe deposit of Yamal-Nenets Autonomous District are realized. For calculations the elastic-plastic model with the Mohr-Coulomb yield condition are used. First it is assumed that the fault remains as elastic. Then gradually transition of various parts of fault to the plastic state is performed. It is assumed that the fault zone are softening after the peak of strength, i.e. the strength decreases with increasing of inelastic deformation until the stress are reached the some residual level. Slipping of fault sides leads to the formation of local subsidence of the surface. It is established that in the case of deposit located at the great depth (about 4km for Ekofisk deposit), we can expect significant surface subsidence, whereas the shallow deposits as in the case of Russcoe deposit at the depth about 1 km, the contribution of the faults is small. The reason is that when the deposit is the deeper the the initial elastic energy accumulated on the fault is greater. So than more energy is released at the fault then the more displacements we can expect.