Magma fluxes in the crust control the thermal viability and mechanical stability of magma chambers.We estimated the magma fluxes required to generate the negative seismic velocity anomaly observed below Soufrie're Hills volcano, Montserrat. Growth of a magma body by accretion of andesitic sills was simulated numerically and the resulting temperatures and melt fractions were used to calculate a synthetic anomaly of seismic wave velocity, which was filtered to be comparable with the velocity anomaly obtained from a tomographic experiment. Petrology indicates that before it was reheated, remobilized and erupted, the temperature of the magma residing in the chamber was about 8508C.We ran simulations where convection is assumed to be low and heat transfer is mostly by conduction and simulations where convection is assumed to be vigorous enough to rapidly cool the magma chamber to 8508C. In both cases, magma chamber growth over the last 350 years results in tomography anomalies that are too strong, unless the magma was emplaced at an unlikely low melt fraction (50·5). Good fits between the modelled and the observed velocity anomaly were obtained with sills 2^5 km in radius emplaced over 6000^150 000 years, depending on the temperature and melt fraction of the emplaced magma. Because of a trade-off between intrusion dimensions and emplacement durations, the volumetric magma fluxes are restricted to 7104 and 5103km3 a1. The velocity anomaly can be reproduced with a chamber containing high melt-fraction magma or with a mush of crystals and melt.The range of magma ages in the modelled magma chamber is much wider than the crystal residence time of the erupted andesite.This suggests that the eruption taps small pockets of recently assembled magma and that the velocity anomaly is mostly due to a non-eruptible mush.