Adaptation of existing solutions to the problem of edge and screw dislocations, which propagate with constant velocity along the fault plane, leads to very compact expressions that can be used as elementary solutions in the construction of near-field motions from arbitrarily complicated faulting in a uniform material. Two obvious limitations, two-dimensionality and the approximation of the free surface, may not be as severe a restriction on the applicability of the method as commonly assumed. Application of the method includes calculation of a profile of displacement, velocity, and acceleration wave forms over a dipping thrust fault. The variation of peak amplitudes with distance for these profiles suggests that the difference in intensity of ground motion on either side of a dipping fault decreases with an increase in the predominant frequency of the motion; hence, particle velocity shows less difference than particle displacement. Other applications include interpretations of near-fault strong-motion recordings. These studies point up the importance of the component of motion perpendicular to the fault. The amplitude of this motion is a strong function of the ratio of rupture to shear velocity and can dominate the near-field motions. As a final application, the spectra of the motions show that the simple near-field spectrum proposed by Brune (1970) on the basis of instantaneous rupture does not hold, even for the parallel component of motion at a small distance from the fault. Brune's modifications for finite rupture propagation seem to be qualitatively correct: the modulation produces an additional ω−1 factor in the spectrum. This will have the effect of limiting the maximum particle acceleration, which, according to simple source theory, can be infinite even with modest stress drops.