This paper describes the simulation methodology adopted to model the mechanical response of Copper single crystals subjected to dynamic loading in different crystallographic orientations. Crystal Plasticity Finite Element Simulations are performed to explain the observed plastic anisotropy in terms of stress-strain response and deformed shapes in [100] and [110] directions. The crystal plasticity model used is based on the thermally activated theory for plastic flow and an evolution equation for slip system deformation resistances incorporating self and latent hardening. The hardening parameters of the model are obtained by calibrating against the previous experiments. The computed stress-strain responses and the deformed shapes agree well with the experimental data.