The finite element analysis of cold flat rolling has been carried out by a number of researchers using updated Lagrangian and flow formulations. The major difficulty in the flow formulation is the estimation of hydrostatic stress accurately. In this work, a mixed pressure-velocity finite element flow formulation is used in obtaining the velocity field during the rolling process. The hydrostatic stress is obtained by solving the momentum equations using a finite difference method. The values of Levy–Mises coefficient and strain-rate components required in the finite difference equations are obtained as a function of spatial coordinates using a radial basis function neural network modeling. The proposed method is compared with a mixed pressure-velocity finite element method and experimental results available in the literature. It is observed that the proposed method provides a better agreement with the experimental results.