For problems involving work-hardening plastic materials, the incremental stress-strain law is considered to be a more rational approach than the conventional total stress-strain law. Up to the present the incremental stress-strain law was not subject to widespread use because it is mathematically inconvenient to handle. In this paper a method is developed in which the incremental law is applied to a work-hardening material in plane stress corresponding to the yield condition of von Mises. The method is illustrated by an analysis of the plastic bending of a simply supported work-hardening circular plate under uniformly distributed transverse load. The resulting difference-differential equations are solved by the NCR 304 digital computer.