Large earthquakes near active volcanoes, that exhibit non-double-couple source properties are usually interpreted as the result of either magma intrusion or geometrical complexity along the fault plane. Such an earthquake occurred in 1996 September 29 at Bárdarbunga volcano in central Iceland, to be followed 2 days later by a major volcanic eruption at the area between Bárdarbunga and the nearby Grimsvötn volcano. Both of these active volcanic centres lie underneath the Vatnajökull glacier, a permanent ice cap that covers a large area of central Iceland. This event was recorded by a temporary network (HOTSPOT) that consisted of 30 broad-band three-component seismometers covering most of Iceland. The waveforms of this event at all stations show an emergent, low-amplitude, high-frequency onset that is superposed on a longer-period signal. The corresponding amplitude spectra show a low-frequency content (<1 Hz) and prominent peaks around the corner frequency (∼0.25 Hz) and higher frequencies. These regional waveforms were inverted in order to obtain the best-fitting deviatoric and full moment tensor using a linear, time-domain inversion method. The results for the daviatoric moment tensor indicate a large (∼60 per cent) compensated linear vector dipole (CLVD) component, a hypocentral depth of 3.5 km, a moment magnitude of 5.4 and a best double-couple solution showing thrust motion in good agreement with the previously published Harvard CMT solution. The results for the full moment tensor on the other hand, indicate an implosive isotropic component of 8.5 per cent, a reduced CLVD component of 47.2 per cent and a best double-couple solution showing normal faulting. However, a statistical F-test revealed that the full moment tensor does not fit the data significantly better than the deviatoric at a confidence level of not more than 76 per cent. All of these results were found not to change substantially when a different source time function was used or when the data were weighted according to their distance from the source. The data are consistent with an earthquake of this magnitude, caused by the failure of an asperity and the formation of a tensile crack due to increasing fluid pressure. The dimensions of the crack may have been 10 x 3 km2 and 0.5 m thickness and the volume of the injected fluid was found to be 15 x 106 m3. The calculated viscosity for the fluid (0.04 Pa s) points to the possibility of water being injected rather than magma, that is also supported by the short source duration of the earthquake (∼5 s . Taking into account the water saturation of the upper crust in Vatnajökull due to the presence of the glacier, this event may have been caused by increased pressure of water that was heated by magma injected through a dyke below the asperity.