The paper represents results of computer modeling of texture formation in pure copper subjected to severe plastic deformation (SPD) realized by equal channel angular pressing (ECAP). Several polycrystalline models, namely the Taylor model, Sachs model, and self-consistent viscous plastic (VPSC) model, were applied and their predictions of texture evolution for different routes and number of ECAP passes were compared. For these calculations, simple shear deformation was used for the deformation realized by ECAP. Using the VPSC model, a single ECAP pass was revisited, but employing a 3D model of material flow, conducted by the variation-difference method, for the ECAP deformation. The influence of the inner and outer radii at the channel intersection and the friction coefficient on the homogeneity of the texture development in the cross section of the bulk ingot was investigated.