Near-field ground displacements are calculated from an earthquake source in a homogeneous, elastic half-space. An analytical formulation of the problem is presented that requires no physical approximations except at the source. A model of the source is constructed by retaining the essential kinematic character of the faulting process. A computer program is developed to calculate ground motion from an assumed model of the 1966 Parkfield, California earthquake. Favorable agreement is obtained between the theoretically computed ground displacements and those derived from the recorded accelerations. The relative contributions of the body waves and surface waves to the displacement field are examined. The results indicate that a significant portion of near-field motion may consist of surface waves, especially in the vertical component of the ground motion.