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We invert intra-eruptive ground displacements recorded between 2003-2005 on Montserrat to shed light on the magmatic plumbing system of Soufrière Hills Volcano. Incorporating 3-dimensional crustal mechanical and topographic data in a finite-element model we show that the recorded displacements are best explained by a southeastward dipping (plunge angle of 9.3˚) vertically extended tri-axial ellipsoidal pressure source with semi-axis lengths of 1.9 and 2.0 km horizontally, and 5.0 km vertically. The source is centred at 9.35 km depth below main sea level and embedded in independently imaged anomalously weak crustal rocks. The source orientation appears to be controlled by the local stress field at the intersection of two major WNW-ESE and NW-SE striking tectonic lineaments. We derive an average volumetric strain rate of 8.4 x10-12 s-1 by transcrustal pressurisation which may have contributed to flank instability and mass wasting events in the southern and eastern sectors of the island.