Ground motion produced by finite, kinematic fault surface is modeled at the surface of a homogeneous half-space. The Green's functions for point dislocations are summed to investigate the effects of different rupture velocities and source rise times. Displacements and velocities are compared for a bilateral and unilateral rupture. The method is used to model the displacements for a laboratory experiment involving a dynamic rupture in a homogeneous block of foam rubber. Good agreement between synthetic and model displacements is obtained at distances ranging from zero to somewhat greater than one fault length. The half-space Green's function summation method is then used to model the N65°E (transverse) component of displacement for the 1966 Parkfield earthquake. The 26-cm displacement pulse on this record is fit with a buried dislocation of 100 cm over a rectangular fault 30 km long and 6 km wide, with a depth of 3 km.