A kinematical approach was proposed in a previous paper for predicting the optimal shape and the deformed length of a rigid-plastic metal sheet during cold-roll forming. Because the elastic effects are important in this kind of process, the method has been extended here to elastoplastic materials. In the new formulation, the sheet is still considered as a thin shell and its middle surface is described as a Coons patch depending on one geometrical parameter. Moreover, the material now satisfies a constitutive rate equation in which the corotational rate of stress is used. The Prandtl-Reuss model, including the von Mises yield criterion and the normality flow rule, is used. In order to integrate the elastoplastic constitutive equations, a radial return scheme is adapted so that the plastic power rate is calculated, using a Gauss method. Its minimization gives the optimal shape for a strain hardening elastoplastic material, as well as the optimal velocity field. This approach has been implemented on a workstation and, as for rigid-plastic materials, it gives a very fast simulation of the cold-roll forming process.