This article gives an overview and analysis of models of plastic deformation of soils and granular materials. It was found that the most frequently used functions are power, logarithmic and exponential, connecting the plastic deformation with the deformation of the first effect of the load or with deformation, accumulated over a certain relatively small number of load applications. Using the theory of hereditary creep generalizing models for calculating the plastic deformation of the cyclic loading were obtained. The proposed method of calculating the residual deformations of granular materials by cyclic loading is integrating the power functions describing the increment of plastic strain. By analyzing the experimental data on the dependence of the residual strain on the number of loads, the maximum and minimum stresses the coefficients of these equations were obtained. The comparison of the calculation results with the experimental data obtained in triaxial test of sand-gravel mixture and granodiorite gravel is presented.