In the work presented here an elastic-plastic crystalline finite element method is used to simulate the cyclic behavior of 316L austenitic stainless steel single crystals and polycrystal. The evolution of the back stress on each slip system is described using a non linear kinematics hardening law to account for the hardening induced by long range dislocation interactions. As the contribution of short range interactions is assumed to be negligible, the value of the friction stress is kept constant. Three dimensional finite element calculations are performed to simulate the cyclic stress strain curves in the case of a single crystal oriented for multiple slips, as well as for the case of the polycristal. Simulations are compared to experimental data. They seem to be satisfactory for low strain values (εp\2 <10-3) whereas, for εp\2 >10-3, they underestimate the hardening observed experimentally.