The method of discontinuous solutions refers to approximate methods of the theoretical investigation of processes of metal working with pressure and does not always provide a result corresponding to reality. Use conditions of the method of discontinuous solutions for studying the plastic pipe crimping process, which ensures a required accuracy, were determined. The method allowed us to take into account geometric parameters of a tool and a billet, the pipe crimping coefficient and other values. The results of the theoretical study are in good agreement with the experimental data and can be used for designing the plastic pipe crimping processes.