A framework for carrying out finite deformation discrete dislocation plasticity calculations is presented. The discrete dislocations are presumed to be adequately represented by the singular linear elastic fields so that the large deformations near dislocation cores are not modeled. The finite deformation effects accounted for are: (i) finite lattice rotations and (ii) shape changes due to slip. As a consequence of the nonlinearity, an iterative procedure is needed to solve boundary value problems. Elastic anisotropy together with lattice curvature is shown to lead to a polarization stress term in the rate boundary value problem. The general three-dimensional framework is specialized to plane strain. The plane strain specialization is implemented in a conventional finite element code and two numerical examples are given: plane strain tension of a single crystal strip and combined bending and tension of that strip. The capabilities and limitations of a conventional finite element framework for this class of problems are illustrated and discussed.