The numerical simulation of rolling processes and its acceleration by model reduction techniques is considered. The physical model is based on minimizing the deformation power by using a flow formulation and the equivalent stress and strain. The reduction uses proper orthogonal decomposition (POD) for linear terms together with the discrete empirical interpolation method (DEIM) for nonlinear terms. In particular, the hardening can be accelerated considerably. The solution can be represented by substantially fewer degrees of freedom while maintaining acceptable accuracy.