Plastic current of sand (destruction fragments of collector) to the well under action of oil inflow and rock pressure is considered. The elastoplastic parameters of sandstone are given as functions of its porosity coefficient. The simple solution, generalizing known Dupuit formula, is offered. Results of the computer calculations which are taking into account effects of collector hardening are delivered. Dependence of sand production on pore pressure drop, cohesion and dilatancy of pay zone matrixes is shown. Zones of compaction and loosening in a zone, localization bands of deformations, and cavities at a perforation hole that essentially influence on intensity of sand production are revealed.