Cup drawing of sheet material (carbon steel DC06 and aluminium alloy AA3103-O) is simulated using a Finite Element (FE) method configured as a hierarchical multi-scale model. It performs a two-way simulation of the interactions between the metal flow and the crystallographic textures of the polycrystalline material. In this, the evolution of the deformation textures is simulated by the Taylor and ALAMEL models, and this in every integration point of the FE mesh. The resulting textures have been compared with experimentally measured ones at different positions within the work-piece. An anisotropic constitutive model is used based on the Facet model identified from the current texture in every location by means of the Taylor and/or ALAMEL model. The updating procedure has been highly optimized. Simulated and experimental results (cup profiles, deformation textures) are compared. The effect of texture updating is assessed.