Anisotropic material properties are commonly neglected during moment tensor inversion. On the other hand, anisotropy is a widely observed rock property. We show that anisotropy may greatly influence characteristics of moment tensors. For the inversion we apply a method based on amplitude spectra of waveforms in isotropic media.We investigate effects of anisotropy on seismic moment, moment-tensor components, and apparent slip inclination of dislocation point sources. The direct calculation of moment tensors for shear sources in anisotropic regions shows spurious non-double-couple components that may be mistaken as an indication of (apparent) opening or closing of the fracture plane. On the other hand real volumetric components may be increased but also hidden in the presence of anisotropy. These effects as well as the seismic moment depend on the orientation of the elastic tensor relative to the fault plane and the slip direction. If anisotropy is present near the source but isotropy is assumed during inversion, the properties of the moment tensor can still be obtained in a good approximation. In the case where anisotropy extends to the medium along the ray path, only the fault orientation can be successfully retrieved by inverting qP waves to derive the deviatoric moment tensor. The inversions showthat retrieved moment tensors can deviate systematically from moment tensors of shear and tensile sources expected in isotropic media. Further complications may arise when qS waves are included in the inversion process. We account for near-source anisotropy to re-interpret moment tensors derived for two events at the KTB super deep drill hole, SEGermany. The obtained source mechanisms are close to shear faulting although the moment tensors comprise non-double-couple components.We interpret the volumetric moment-tensor components partly as a result of anisotropy. This indicates that for detailed studies of volumetric source components anisotropy should be considered during inversion. In addition, we show that for shear sources in anisotropic media the elastic properties near the source can also be derived from inverted moment tensors in media where anisotropy is restricted to the source region.