Slip on an undulatory strike-slip fault induces predictable residual stresses in the adjacent crust. Elastic analytic and finite element models are developed to quantify these stresses for arbitrary fault geometries. Across fault-parallel planes, domains of reverse, normal, right-lateral and left-lateral residual stresses are induced near the bends in the fault. These residual stresses increase in magnitude from one slip event to the next, typically reaching failure level after several events. A two-dimensional analytic elastic plate model for slip on a sinusoidal fault provides general results on the scales and patterns of slip-induced stresses, and Fourier synthesis allows for the solution with arbitrary but small fault distortions. Maximum fault-normal residual stress is proportional to the square of the wavenumber of the sinusoidal trace and decays exponentially away from the fault, reduced to 2/e times the maximum value at a distance equal to 1/wavenumber. This fault-parallel residual shear stress oscillates between dextral and sinistral along the fault, with maximum magnitude adjacent to the maximum excursions in the fault trace. Fault-parallel residual shear stress is maximum at a distance from the fault of 1/wavenumber, where its magnitude is 1/e times the maximum normal stress on the fault. Two- and three-dimensional finite element analyses extend the analytic model; they account for depth-decaying fault perturbation amplitude and slip deficit and are valid for large fault undulations. Application of the model to the San Andreas fault in the Cajon Pass region produces the complex distribution of fault-parallel normal, reverse, right-lateral and left-lateral structures recognized near the main trace. Left-lateral stresses on planes subparallel to the San Andreas fault at the Cajon Pass well are predicted by this model. ¿ American Geophysical Union 1992