In contrast to global observations in stable continental crust, the present-day orientation of the maximum horizontal stress in Western Australia is at a high angle to plate motion, suggesting that in addition to large-scale plate driving forces, local factors also play an important role in stress repartitioning. As a reliable stress indicator, full waveform moment tensor solutions are calculated for earthquakes that occurred between 2010 and 2018 in the southern Yilgarn Craton and the adjacent Albany-Fraser Orogen in southwestern Australia. Due to regional velocity heterogeneities in the crust, we produced two geographically distinct shear wave velocity models by combining published crustal velocity models with new ambient noise tomography results. We applied a full waveform inversion technique to 15 local earthquakes and obtained 10 robust results. Three of these events occurred near Lake Muir in the extreme south of the study area within the Albany-Fraser Orogen. The focal mechanism of the 16th September 2018 Lake Muir event is thrust; two ML≥ 4.0 aftershocks are normal and strike-slip. Our results are consistent with field observations, fault orientations inferred from aeromagnetic data and surface displacements mapped by Interferometric Synthetic Aperture Radar which are all consistent with reactivation of existing faults. The other seven solutions are in the southeastern Yilgarn Craton. These solutions show that the faulting mechanisms are predominantly thrust and strike-slip. This kinematic framework is consistent with previous studies that linked active seismicity in the Yilgarn Craton to the reactivation of the NNW-SSE oriented Neoarchean structures by an approximately E-W oriented regional stress field. Our results suggest that the kind of faulting that occurs in southwest Australia is critically dependent on the local geological structure. Thrust faulting is the dominant rupture mechanism, with some strike-slip faulting occurring on favourably oriented structures.