This research applies an accurate and efficient method for analyzing cracks in a three-dimensional elastic half-space to the study of slip zones in the earth's crust. Previous studies are extended to consider the effects of non-uniform stress drop, segmented faults, and coupling of normal and shear stresses due to near-surface slip and non-planar slip zones and advance of slip zones. In addition, calculations are done to determine stresses and surface deformations due to the advance of shear faults into and around locked, or more resistant, portions of the shallow crust. The goal of these studies is to understand better the mechanics of earthquake slip and, in particular, conditions that control the initiation and termination of earthquake ruptures. This research is a component of the National Earthquake Hazard Reduction Program.