The amplitude of the Rayleigh waves produced by a finite, propagating dip-slip fault of arbitrary orientation in a homogeneous, isotropic half-space is obtained. The fault is assumed to initiate suddenly at depth and to spread unilaterally to the free surface with constant speed. The Rayleigh-wave amplitude ahead of the fault break is shown to be considerably higher than that behind the initial epicenter. There is severe amplitude modulation in the epicentral region caused by the interference of waves traveling in opposite directions. The numerical results indicate that for Rayleigh waves in the period range of interest in earthquake engineering, a number of simplifications can be made in modeling an earthquake source of this type.