A therory is proposed for the propagation of seismic surface-waves from finite moving sources. The method consists of obtaining, in the first place, basic solutions for surface displacements from directional sources. These solutions are integrated to obtain the effect of a moving fault with arbitrary dip angle. Displacements are evaluated for Rayleigh and Love waves at long ranges. It is shown that the dimensions of the source and the speed of rupture play an important role in the wave-pattern and cannot be ignored whenever the dimensions of the source are of the order of the radiation's dominant wave-length. It is demonstrated how this theory may lead to a derivation of the velocity of rupture and the length of faulting from seismic records of a single station.