We use the exceptional set of strong ground motion records obtained during one of the largest aftershocks (ML = 5.0) of the 1979 Imperial Valley earthquake to study the time history of rupture on a kilometric size fault. We apply single crack, composite cracks, and dislocation earthquake models to simulate the source and calculate the ground velocity and acceleration at the recording sites. The best fit to the data is obtained for a crack-like source where rupture is initiated at one edge and expands circularly over the fault. The stress drop inferred is 720 bars, and the fractured area has a diameter of about 1 km. The fault is vertical and strikes in the N320°E direction. This simple model explains surprisingly well the amplitudes and waveforms of the ground velocities and accelerations recorded in the near-source region during the event.