Most industrial metal forming processes are characterised by a complex strain path history. A change in strain path may have a significant effect on the mechanical response of metals. This paper concentrates on the role of the plastic slip anisotropy in the strain path dependency of materials containing a dislocation cell structure. The cell structure model, developed in Viatkina et al. [Viatkina, E., Brekelmans, W., Geers, M., 2007. Modelling of the internal stress in dislocation cell structures. Eur. J. Mech. A: Solids 26(6), 982–998], is extended here by employing a crystal plasticity model for describing the local material behaviour. This, more physically based description of the plastic behaviour, allows accounting for plastic anisotropy resulting from the crystal lattice of a metal. The extended cell structure model accounts for four sources of anisotropy: (1) geometrical anisotropy due to the configuration of the cell structure, (2) anisotropy due to the internal stresses associated with the cell structure, (3) slip anisotropy and (4) textural anisotropy. The relative contributions of the four sources of anisotropy are discussed.