For a propagating, vertical, strike-slip fault whose breakage extends to the Earth's surface, previous studies by Aki (1968) and Haskell (1969) have suggested that the near-field motions may be similar to those from uniformly-glidingedge dislocations. The theory of these dislocations in uniform motion leads to a simple, convenient relation between the perpendicular and parallel components of motion at the fault's surface. A number of examples are considered in order to illustrate this relation between the horizontal components. In general, step-function-like parallel motions result in pulse-like perpendicular displacements. For a given parallel displacement, the amplitude of the pulse depends in a concise manner on ratios of the rupture to shear-wave velocity, and on shear- to compressional-wave velocity. Increasing either of these ratios leads to an increased pulse-amplitude. The dislocation model is applied to the near-field observations of the Parkfield earthquake. The resulting estimate of the total fault offset is within the range of those based on the more detailed models of Aki (1968) and Haskell (1969).