An analytical method to evaluate the transient response on the surface of an elastic half-space for a kinematic dislocation over an infinitely long fault of finite width and arbitrary dip is presented. The model includes finite rupture velocities in the direction of both the strike and dip of the fault. In this sense, it differs from previous two- and three-dimensional models which typically assume one of these velocities to be infinite. In addition to the effects of the free boundary, the model considers a slip vector in an arbitrary direction. The assumptions of infinite fault length and uniform rupture velocities account for the relative simplicity of the solution which is invariant to an observer moving along the strike of the fault with a speed equal to the rupture velocity. These assumptions limit the applicability of the solution to near-field locations far from the ends of realistic faults. A limited set of numerical results illustrating the types of pulse shapes obtained by use of this model, and, some tests to validate the derivation and the numerical results are presented.