Sequence of quasistalic solutions of boundary value problems about the viscoelastic deforming, origin and development of plastic flow with the subsequent unloading in a material with a spherical concavity by the viscoelastoplastic body model are given. Before plastic flow origin and at an unloading the material is necessary the linear viscoelastic one, the viscous dissipative mechanism is saved and at plastic flow too. The principal attention is given conditions o f repeated plastic flow origin and influence one on total distribution of residual stresses.