Abstract In this work we develop multi-surface plasticity model which can reproduce the inelastic behavior and failure modes of concrete in tension, compression and shear. The main novelty of the proposed concrete model can also capture all different phases of localized failure for massive structures, where the elastic behavior is followed by the creation of the fracture process zone with a large number of micro-cracks and subsequent final failure mode with micro-cracks coalescence into the macro-crack. The fracture process zone is represented by homogenized plasticity criterion with hardening (in particular the non-associated Drucker-Prager) since the number of micro-cracks is considered sufficiently large and their orientation random. The macro-crack is represented with a surface of displacement discontinuity, which is typical of all localized dissipative mechanisms due to the apparition and development of localization zones. The main novelty of proposed model is to provide the full set of 3D localization modes for tension, for compression and for shear, with each mode using corresponding fracture energy.