This paper investigates the role of a nonzero vapour entry pressure on reservoir storage and containment of the greenhouse gas carbon dioxide. Two effects are observed: vapour storage under confining layers, and enhanced lateral spreading of gas under confining layers. Lateral flow of gas under both impermeable and permeable confining layers is solved analytically using Buckley-Leverett assumptions. A full numerical analysis of gas and water transport is also presented, using results from the simulator TOUGH. We consider the injection of CO2 from a thermal power plant at a rate of 100 kg/s for 10 years, at a depth of 3000 metres. Inclusion of a nonzero vapour entry pressure shows that containment of this gas for at least 5000 years can be expected. The CO2 is stored predominantly in a high density vapour phase (about 600 kg/m(3)) under lower permeability confining layers, and also is dissolved in liquid at about 40 kg/m(3).