When a fault occurs in the earth's crust, the ground in its vicinity becomes deformed. This thesis uses the theory of dislocations, as developed by J. A. Steketee, to examine the nature of this deformation for a variety of strike-slip fault models. The theory is developed for calculating the displacement field and stress changes expected at any point around a vertical transcurrent dislocation surface whose net displacement is constant in the horizontal direction, and varies with depth. The results obtained are compared graphically with geodetic data, and those discrepancies that arise between theory and observation are attributed to the limiting assumptions of the model. The principal conclusion of this work is that the variable-slip fault model provides a significant improvement over previous fault models which assumed a constant displacement.