Modern crystal plasticity methods take advantage of dislocation dynamics simulations to accurately model material deformation in support of computational materials design. However, there are presently no accurate and computationally efficient methods for modeling the stress and strain fields associated with dislocations in the vicinity of arbitrary free surfaces. This is a source of error in modeling dislocations for applications like MEMS, where small length scales and complex geometry make an infinite or semi-infinite assumption troublesome. This proposal is to develop mathematical and efficient computational techniques for modeling dislocations in elastic volumes of arbitrary shape. There are already published solutions for a few such cases (semi-infinite volumes, space between two parallel planes, etc.) and this study will seek to generalize those methods. These methods will be validated using atomistic simulations and electron microscopy on MEMS devices with well-characterized dislocation structures. Since dislocations are critical to both plasticity and failure modes in crystalline materials, this research has implications in computational design and failure prediction on subjects with length scales on the order of several microns and smaller.