The behaviour of an inviscid, lock-released gravity current which propagates over a horizontal porous boundary in either a rectangular or an axisymmetric geometry is analysed by both shallow-water theory and ‘box-model’ approximations. It is shown that the effect of the porous boundary can be incorporated by means of a parameter λ which represents the ratio of the characteristic time of porous drainage, τ, to that of horizontal spread, x0 =(g′h0)1/2, where x0 and h0 are the length and height of the fluid initially behind the lock and g′ is the reduced gravity. The value of τ is assumed to be known for the fluid–boundary combination under simulation. The interesting cases correspond to small values of λ; otherwise the current has drained before any significant propagation can occur. Typical solutions are presented for various values of the parameters, and differences to the classical current (over a non-porous boundary) are pointed out. The results are consistent with the experiments in a rectangular tank reported by Thomas, Marino & Linden (1998), but a detailed verification, in particular for the axisymmetric geometry case, requires additional experimental data.