Abstract Generalized continuum models are becoming common in studies aiming at capturing the heterogeneous character of the deformation of granular rocks. Their constitutive equations take into account characteristics of the microstructure of the material which regularize the mathematically ill-posed problem of strain softening plasticity and lead to scale effect in boundary value problems. Two of the most prevalent models, the Cosserat and the second-gradient plasticity models are compared on the basis of their ability to describe the experimentally observed scale effect in hollow cylinder experiments.