Shear strain localization refers to the phenomenon of accumulation of material deformation in narrow slip zones. Many materials exhibit strain localization under different spatial and temporal scales, particularly rocks, metals, soils, and concrete. In the Earth's crust, irreversible deformation can occur in brittle as well as in ductile regimes. Modeling of shear zones is essential in the geodynamic framework. Numerical modeling of strain localization remains challenging due to the non-linearity and multi-scale nature of the problem. We develop a numerical approach based on graphical processing units (GPU) to resolve the strain localization in two and three dimensions of a (visco)-hypoelastic-perfectly plastic medium. Our approach allows modeling both the compressible and incompressible visco-elasto-plastic flows. In contrast to symmetric shear bands frequently observed in the literature, we demonstrate that using sufficiently small strain or strain rate increments, a non-symmetric strain localization pattern is resolved in two- and three-dimensions, highlighting the importance of high spatial and temporal resolution. We show that elasto-plastic and visco-plastic models yield similar strain localization patterns for material properties relevant to applications in geodynamics. We achieve fast computations using three-dimensional high-resolution models involving more than 1.3 billion degrees of freedom. We propose a new physics-based approach explaining spontaneous stress drops in a deforming medium.