A potential-based panel method is presented for the analysis of a partially or supercavitating two-dimensional hydrofoil at a finite submergence beneath a free surface, treating without approximation the effects of the finite Froude number and the hydrostatic pressure. Free surface sources and normal dipoles are distributed on the foil and cavity surfaces, their strength being determined by satisfying the kinematic and dynamic boundary conditions on the foil-cavity boundary. The cavity surface is determined iteratively as a part of the solution. Numerical results show that the wave profile is altered significantly due to the presence of the cavity. The buoyancy effect due to the hydrostatic pressure, which has usually been neglected in most of the cavitating flow analysis, is found playing an important role, especially for the supercavitating hydrofoil; the gravity field increases the cavity size in shallow submergence, but decreases when deeply submerged, while the lift is reduced at all depth.