The source characteristics of 10 shallow earthquakes of moderate size (M>5) beneath Bárdarbunga Volcano in Iceland are investigated using long-period and broadband teleseismic data. The highly non-double-couple nature of the focal mechanisms for several of the events previously reported in the Harvard centroid moment tensor (CMT) catalog is confirmed by analysis of an expanded long-period body wave data set, as well as by an independent inversion of intermediate period surface wave data. Modeling of broadband P waveforms constrains the depths of the events to lie between 3 km and 8 km beneath the volcano. Significant complexity in the P waves observed for some events is best explained by a sequence of subevents of varying geometry, rather than by wave propagation effects caused by shallow structure near the earthquake. Inversion of P wave data for two of the earthquakes using a parameterization with subsources results in sequences of events with primarily thrust motion on planes of varying strike. The seismological results are interpreted as faulting on an outward dipping cone-shaped ring fault beneath the Bárdarbunga caldera. The association in time and space between the September 29, 1996, earthquake and the September 30 eruption near Bárdarbunga and Grimsvötn Volcanos suggests that inflation of a shallow magma chamber, and the associated stress loading of the deeper ring fault, may be the tectonic process which generates the earthquakes.