A model for strain gradient crystal visco-plasticity is formulated along the lines proposed by Fleck andWillis (2009) for isotropic plasticity. Size-effects are included in the model due to the addition of gradient terms in both the free energy as well as through a dissipation potential. A finite element solution method is presented, which delivers the slip-rate field and the velocity-field based on two minimum principles. Some plane deformation problems relevant for certain specific orientations of a face centered cubic crystal under plane loading conditions are studied, and effective in-plane parameters are developed based on the crystallographic properties of the material. The problem of cyclic shear of a single crystal between rigid platens is studied as well as void growth of a cylindrical void.