The behaviour of an inviscid gravity current which is released from behind a lock and then propagates over a horizontal boundary at the base of a stratified ambient fluid is considered. An extension of the shallow-water formulation for a homogeneous ambient to the stratified case is developed, without using any additional adjustable parameters. Attention is focused on the initial ‘slumping’ stage of a rectangular current which is typified by a constant speed of propagation. The analytical results are in good agreement with, and give a firm theoretical interpretation of, the corresponding experiments and numerical simulations of Maxworthy et al. (2002). Finite-difference solutions of the Navier–Stokes equations, using a different technique from that used by Maxworthy et al. (2002), are also presented and provide both good agreement with their results and further validation of the present shallow-water approach. The differences between currents in a homogeneous and stratified ambient, and possible implementation of the results to other configurations, are discussed.