We propose a new theory for non-elastic deformation of a granular medium. The theory takes into account both elastic and plastic deformations. Structurally, the theory proposed is similar to the theory of deformation theory of plasticity of metals. Using the theory proposed, we have an opportunity to solve elastic-plastic problems with less difficulty and to trace the transfer from pure elastic state to the state of ultimate equilibrium. We solve an elastic-plastic problem for a thick-walled circular cylinder under the action of external pressure. A value of the limiting load obtained as a result of corresponding passage to the limit is in good agreement with the results by A. Nadai that was obtained on the bases of the theory of ultimate equilibrium. We state and solve a new elastic-plastic static problem for a circular layer with a hole (well) in its center. It should be mentioned that there is no opportunity to solve the last problem in the framework of the theory of ultimate equilibrium.