A method to calculate the response on the surface of a multilayered half-space for a fault of finite width and infinite length is presented. The model involves a piecewise-rectilinear and continuous rupture front propagating at a constant rupture velocity along the length of a fault of arbitrary dip angle. The motion produced by this steady state dislocation model corresponds to the passage of the rupture front phase, which is a predominant phase in the near-source records. A series of validation tests, using both three- and two-dimensional kinematic fault models, and a limited set of parametric studies clarifying the mechanisms involved in the generation of high amplitudes, are presented. Finally, it is shown that the distribution of peak horizontal velocities in the near-source region calculated by use of a steady state model in a layered medium compare favorably with the regression results of Joyner and Boore (1981). ¿ American Geophysical Union 1988