The supercavitating flow past slender delta wings is studied. Theory is developed for a conical flow involving cavities which spring from the leading edges of the delta and cover a part of the top of the wing; the center part of the wing top is assumed to be wetted by a kind of re-entrant jet flow. Results are obtained for the two separate asymptotic cases in which the cavitation number is either very small or very large. The widths of the cavities on the wing upper surface increase with decreasing σ and the lift decreases. It is shown that the upper surface never becomes completely enveloped in a cavity even for σ = 0. Finally, the lift of a fully cavitated wing (σ = 0) is estimated to be approximately 4/10 of its fully wetted lift.