Using 3D Green’s functions we determine full and constrained moment tensor solutions of icequakes near the base of Gornergletscher, Switzerland. The seismic events were recorded in the summer of 2004 using a high-density seismometer array. The seismic velocity model used in the generation of Green’s functions is based on radio-echo soundings to approximate the basal topography, which beneath the study site exhibits a strong inclination. As the basal conditions are not well known, we try moment tensor inversions with seismic velocity profiles consisting of two and three media. The former case consists of homogeneous ice resting on bedrock, whereas the latter case includes a thin basal layer with slow seismic velocities representing eroded material or highly fractured ice. Effects of errors in Green’s functions are estimated by sensitivity studies in which we invert 1D and 3D synthetics using Green’s functions of wrong velocity models. The results show that calculations of source types and fault plane orientations of tensile cracks are rather robust with respect to errors in Green’s functions. However, the quality of the waveform fits depends on strike and dip of the synthetic source. When inverting seismograms, Green’s functions of the seismic model that includes the basal slow velocity layer are found to give the most realistic source types as well as the best waveform fits. The fault mechanisms derived from constrained moment tensor inversions are near-horizontal tensile cracks, which suggest a complex time-dependent basal stress field.