An analytical solution to the equations describing the flow of a buoyant fluid released into a porous medium below a horizontal impermeable boundary is used to model the growth of CO2 accumulations beneath thin mudstone beds in the Utsira sand reservoir at Sleipner in the North Sea. Here supercritical CO2 has been injected at a rate of ab. 1 MT/yr since 1996 and imaged by time-lapse seismic data in 1999, 2001 and 2002. The CO2 rises as a narrow plume and is partially trapped by a number of thin mudstones before reaching the caprock to the reservoir. The radii of the individual layers of trapped CO2 increase as the square root of time since initiation as predicted by the modelling for constant input flux. However apparent negative initiation times for horizons low in the reservoir suggests that net input fluxes for these layers have decreased with time, most probably as the spreading layers have increased their leakage rates. Accumulation of CO2 in the layers higher in the reservoir was initiated up to 3 yr after injection started. Modelling of the thickness profiles across three of the higher layers suggests that their net input fluxes have increased with time. The observation that the central thicknesses of the deeper layers have remained approximately constant, or have slightly decreased since first imaged in 1999, is consistent with the model predictions that the central thickness is directly proportional to net input flux. However, estimates of the permeability of the reservoir from the rate of increase of the radii of the CO2 accumulations are an order of magnitude less than measured permeabilities on the reservoir sandstone. Permeabilities estimated from the modelling of layer thickness changes scatter in the same range. These discrepancies may arise from, 1) approximations in the model not being valid, 2) the measured permeabilities not being representative of the permeability for two-phase flow on the scale of the reservoir or, considered less likely, 3) that much less CO2 is being stored in the imaged CO2 accumulations than estimated from the seismic reflection profiles. The most probable cause of the discrepancy is that the relative permeability for the CO2 phase is significantly reduced at lower CO2 saturations