This paper deals with description of the deformation process in argillaceous rocks that display a strong inherent anisotropy. Both, the homogeneous and the localized deformation modes are considered. The effects of anisotropy are incorporated by invoking the microstructure tensor approach. The strain localization is assumed to be associated with formation of a macrocrack the orientation of which is defined using the critical plane approach. The propagation of damage is traced within the context of a boundary value problem by employing a constitutive law with embedded discontinuity. The crack path is monitored in a discrete manner by using the level-set method. The closest-point projection algorithm is developed for the integration of the constitutive relations at both stages of the anisotropic deformation process, i.e. the homogenous mode as well as that involving an embedded discontinuity. The problem of macrocrack formation in a biaxial plane strain compression test is studied. It is demonstrated that friction between loading platens can play an important role in the process of evolution of damage and may significantly affect the compressive strength.