Strain localization in the form of compactive shear bands or compaction bands is often observed in high porosity rocks such as sandstones or limestones. In the present study, we theoretically investigate the possibility of strain localization in a high-porosity carbonate rock (calcarenite) by means of a continuum mechanics approach. A critical state elasto-plastic constitutive model has been employed for this purpose. We examine the constitutive and structural response by solving boundary value problems (BVPs) for calcarenite specimens subjected to axisymmetric loading conditions. In order to perform the numerical simulation in the post localization regime, the model is enhanced with a rate dependent regularization scheme. The results demonstrate that material heterogeneity, kinematic constraints and boundary effects govern the formation of various modes of localized deformation in the transitional regime between brittle fracture and ductile faulting. Indeed, the predicted macroscopic response is found to be in good agreement with observations available in the literature.