Using a density matrix renormalization approach we have calculated the phase diagram of a two-dimensional Ising model confined between two infinite walls, with opposing surface fields and a bulk field which grows linearly as a function of the distance from the walls and models the effect of gravity on a confined fluid. In the absence of gravity, two-phase coexistence is restricted to temperatures below the wetting temperature as pointed out by Parry acid Evans [A.O. Parry, R. Evans, Phys. Rev. Lett. 64, (1990) 439]. We find that the competing effects of gravity and surface fields restore the ＇ordinary＇ finite size scaling to the bulk critical point, in agreement with previous mean-field results. We have calculated the exponents related to the shift toward the critical point in the limit L --> infinity, where L is the distance between the walls and we have found good agreement with previous scaling assumptions. Magnetization profiles calculated from a solid-on-solid Hamiltonian agree well with density matrix renormalization results for temperatures not too close to the bulk critical temperature. (C) 1998 Elsevier Science B.V. All rights reserved.