This research is motivated by the increasing need for geostorage facilities such as nuclear waste disposals, high-pressure gas reservoirs and carbon dioxide sequestration systems. Salt rock has favourable creep properties, enabling crack healing in relatively low-pressure and low-temperature conditions. Contrary to models proposed in continuum damage mechanics, creep models can predict damage increase and decrease. However, the formulation does not allow the modelling of time-independent crack opening and the resulting anisotropy of stiffness and deformation. Moreover, a distinction needs to be made between reversible and irreversible crack-induced deformation. A compression test including a healing phase has been simulated using a model in which healing of deformation and stiffness recovery are not clearly distinguished. The results show an inconsistency between deformation and healing evolutions. To overcome this problem, an alternative modelling framework is proposed to predict anisotropic healing deformation and stiffness recovery.