[en] In this paper, we present a new one-point integration method generalizing Flanagan and Belytschko's method (Internat. J. Numer. Methods Engrg. 17 (1981) 679-706) and a modification of Belytschko and Bindeman's method (Comput. Methods Appl. Mech. Engrg. 88 (1991) 311-340), both in the frame of large deformation elastoplastic analysis. These stabilization methods are combined with the radial return method used to integrate the constitutive law. Plane strain problems are first considered, and the method is then generalized to axisymmetrical situations. The explicit time integration scheme with its critical timestep is also considered. A few examples are presented that show the great time savings that can be obtained with reduced integration without any loss of accuracy, and even with a gain in the solution quality, since the underintegrated elements prove to be 'flexurally superconvergent'.