This study deals with the influence of the rolling asymmetry and applied strain on the crystallographic texture of polycrystalline copper. It was shown that textures of asymmetrically rolled materials are rotated with respect to those rolled symmetrically and the rotation angle increases both with the rolling asymmetry and strain. The asymmetric rolling leads also to a decrease of intensity of texture components forming skeleton lines in the orientation space. However, individual texture components exhibit different sensitivity to the effect of asymmetric rolling.