This study explores the development of irreversible deformation from the tips of an internal defect in rock under cyclic loading within an elastic-viscoplastic framework. Nonlinear stress-strain curves are obtained which show hysteresis loops and a stage where stresses decrease with continuing deformation. It is shown that irreversible deformation and failure of the sample under cyclic loading can occur without increasing the level of the applied load. Zones of residual stresses during unloading are located next to the areas of stress concentration at the active stage of loading. Numerical modeling was carried out in 2D and 3D formulations using original numerical codes.