Despite crystals’ widespread use in industry and technology as well as their structural simplicity, there is still the need for new multi-scale fundamental theory of crystal plasticity bridging the atomic scale and the continuum description. Some models and methods such as Discrete Dislocation Dynamics, Phase Field Methods and the Quasi-Continuum Method have been successful by capturing some of the features of crystal plasticity at the mesoscale. However, prohibitive computational requirements, tedious numerical implementations or modeling assumptions may limit these methods to specific use-cases. The Mesoscopic Tensorial Model (MTM) of crystal plasticity[1] has shown to be able to capture phenomena in 2d such as nucleation and annihilation of dislocations, pattern formation and avalanches[2] while providing a new self-consistent understanding. The model’s main ingredients feature the GL(3,Z) group symmetry, non-linear elasticity and the Cauchy-Born rule enabling for a fully coarse-grained understanding. The model thus only requires initial knowledge of the material’s crystal symmetry and inter-atomic potential. We will show in this work how to construct a 3D version of MTM, its ability to reproduce many of the fundamental mechanisms of crystal plasticity in particular in Face-Centered Cubic crystals, such as spontaneous dislocation splitting, interaction between dislocations and (homogeneous) nucleation of dislocation avalanches and the renewed understanding of these phenomena with MTM.