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Crystallographic texture development during asymmetric rolling of three different metals (aluminum, copper and titanium [1,2]) was investigated experimentally and modeled using Finite Element Method (FEM) and crystalline plasticity (CP) models. The rolling asymmetry was induced by difference in the rolls diameters or by the difference in angular velocities of two identical rolls. In one case the rolling asymmetry was also induced by selection of the insertion angle of the rolled band between the rolls (i.e., tilted material entry). Crystallographic texture variation over the rolled bar thickness was determined using X-ray diffraction and predicted using FEM+CP modelling. The dominating effect in asymmetric rolling is texture homogenization across the sample depth, caused by the occurrence of strong shear stress and strain components in the material. The changes in texture distribution also affect mechanical parameters of the material, especially the plastic ductility. The latter one, expressed by the increase of the maximal strain at fraction, is correlated with texture homogenization. The elaborated software can be used to optimize the rolling geometry process. The best rolling variants, recommended for the technological practice, are indicated.