Results of a 2-D, seismic undershooting experiment on the Katla central volcano in south Iceland are reported. Large localized traveltime anomalies (0.4s) are observed on an array within the Katla caldera. the traveltimes are forward modelled using a wavefront tracker developed in Appendix A. Thus, non-linear effects encountered in traveltime tomography are avoided as well as common problems with ray tracing in the presence of strong lateral heterogeneity. an extreme variation in compressional velocity is required to extend over a significant volume in order to model the data. the resulting model is not unique, but constraints on the allowable range of velocities (2.5-6.0 kms−1) render the basic features well constrained. A clear S-wave shadow is closely associated with delays in traveltime due to a shallow slow anomaly. Low-amplitude P waves go hand in hand with early arrivals due to thin structural features flanking the slow anomaly. the model is interpreted in terms of a magma chamber containing extensively molten rock. the magma chamber is shallow, with a bottom at a depth of about 1.5km below sea-level (3.0 km below surface), and measures about 5 km across. the depth of the chamber is roughly at the level of buoyant equilibrium for basaltic melt in the crust. Owing to poor vertical resolution at shallow depths in the undershooting geometry the top of this shallow magma chamber is not well resolved. On the other hand, the bottom of the chamber is well resolved. the chamber is underlain by rocks of average or high velocity for that depth. the magma chamber is a persistent feature, big enough (10km3) to supply magma for large eruptions and to supply heat to permit remelting of hydrated basaltic crust to produce silicic magmas at shallow levels. the chamber is fed by magma fracturing from below. the model agrees with phenomenological models of magma chambers in Iceland based on geological observations and provides a quantification of those models in terms of depth and size. On the other hand, it is fundamentally different from recent models of magma chambers at mid-ocean ridges which may be more akin to the pervasive region of partial melt at depth beneath Iceland. This underlines the important effect of the Icelandic hotspot on tectonics and volcanism in Iceland and implies a substantially different crustal and thermal structure in Iceland from that of ‘normal’ mid-ocean ridges.