Аннотация:The problem of fluid filtration into a producing well in a reservoir withthe properties depending on the stress-strain state is studied. The primary attentionis devoted to anisotropy of the strength properties of reservoir rocks and to theinfluence of fluid pressure on the redistribution of stresses in formation. The problemis solved for two variants of the bottomhole design: an open hole and a hole with twodiametrically opposed vertical cuts. The first variant, corresponding to a relativelysimple geometry, allows to obtain solution qualified for comparison with analyticalone.