Surface deformations recorded in close proximity to the active lava dome at Soufri¿re Hills volcano, Montserrat, can be used to infer stresses within the uppermost 1000 m of the conduit system. Most deformation source models consider only isotropic pressurisation of the conduit. We show that tilt recorded during rapid magma extrusion in 1997 could have also been generated by shear stresses sustained along the conduit wall; these stresses are a consequence of pressure gradients that develop along the conduit. Numerical modelling, incorporating realistic topography, can reproduce both the morphology and half the amplitude of the measured deformation field using a realistic shear stress amplitude, equivalent to a pressure gradient of 3.5 ¿ 104 Pa m-1 along a 1000 m long conduit with a 15 m radius. This shear stress model has advantages over the isotropic pressure models because it does not require either physically unattainable overpressures or source radii larger than 200 m to explain the same deformation.