A least squares method is proposed to invert Rayleigh and Love wave observations in source mechanism studies. When complex spectra is available the inversion scheme is linear and it is carried out in a single step. When only amplitude spectra is available the inversion scheme may be linearized and it converges to a unique solution independent of the orientation of the initial trial source. Source depth is found by minimizing errors in repeated application of the method at different trial depths. Application to real data requires a careful weighting of observations when the path structure is not well-known. Th source representation in terms of seismic moment tensor components allows for a simple analysis of the surface wave data resolving power. Complex spectra of Rayleigh waves render a unique solution, but complex spectra of Love waves admit infinite solutions. If a double-couple source is assumed, the Love wave data may have either one or three equally satisfactory solutions. When only absolute vales of surface wave spectra are available, any solution may be rotated 180¿ in azimuth and/or all the source tensor components may be changed in sign.