||This paper presents a mathematical framework for modeling the creep phenomenon in frictional materials exhibiting a strong inherent anisotropy. The instantaneous time-independent response is described by invoking a plasticity framework which incorporates a scalar anisotropy parameter. The latter is a function of mixed invariants of the stress and microstructure tensors. The creep is assumed to be associated with progressive rearrangement of material structure. The evolution of the elastic compliance is established based on a homogenization procedure for periodic media. In the plastic range, the problem is formulated in terms of evolution of the eigenvalues of the microstructure tensor, while the eigenvectors are preserved. The framework is applied to investigate the creep characteristics of sedimentary rocks, which exhibit a transverse isotropy. In particular, a numerical analysis is carried out to examine the basic trends in the mechanical response of Tournemire shale.