The theory of thermally-activated slip is used to derive a crystal-plasticity materials constitutive model for deformation of OFHC copper single crystals. The mechanical response of the polycrystalline material is next determined from the single-crystalline materials constitutive relations using the classical Taylor approximation for apportionment of the deformation gradient between grains. Simulations of the deep drawing of cylindrical cups from as-rolled OFHC-copper blanks are next carried out using an explicit finite element formulation. The results obtained show that the crystallographic texture in as-rolled sheets, which can be accounted for through the use of crystal-plasticity, gives rise to rim-earing in fully-drawn cups. It is further shown that the extent of rim-earing can be greatly reduced by properly modifying the shape of the blank. A procedure is next proposed for optimization of the blank shape.