A Taylor-type polycrystalline model, together with a new fully-implicit time-integration scheme has been developed and implemented in a finite element program to simulate the evolution of crystallographic texture during bulk deformation processing of face centered cubic metals deforming by crystallographic slip. The constitutive equations include a new equation for the evolution of slip system deformation resistance which leads to macroscopic strain hardening behavior that is in good accord with experiments performed on OFHC copper. The good predictive capabilities of the constitutive equations and the time-integration procedure for simulating the stress-strain behavior and the evolution of texture under both homogeneous and non-homogeneous deformation conditions are demonstrated by comparing numerical simulations against experimental measurements in simple shear and a simple plane-strain forging experiment on copper.