A rate-dependent self-consistent crystal plasticity model was incorporated with the Marciniak–Kuczyński model in order to study the effects of anisotropy on the forming limits of BCC materials. The computational speed of the model was improved by a factor of 24 when running the simulations for several strain paths in parallel. This speed-up enabled a comprehensive investigation of the forming limits of various BCC textures, such as , , , and fibers and a uniform (random) texture. These simulations demonstrate that the crystallographic texture has significant (both positive and negative) effects on the resulting forming limit diagrams. For example, the fiber texture, which is often sought through thermo-mechanical processing due to a high r-value, had the highest forming limit in the balanced biaxial strain path but the lowest forming limit under the plane strain path among the textures under consideration. A systematic investigation based on the results produced by the current model, referred to as' VPSC-FLD', suggests that the r-value does not serve as a good measure of forming limit strain. However, model predictions show a degree of correlation between the r-value and the forming limit stress.