Extending the Swendsen-Wang cluster algorithm to include both bulk (H) and surface fields (H-1) in LxLxD Ising films of thickness D and two free LxL surfaces, a Monte Carlo study of the capillary condensation critical point of the model is presented. Applying a finite-size scaling analysis where the lateral linear dimension L is varied over a wide range, the critical temperature T-c(D) and the associated critical field H-c(D) are estimated for 4 less than or equal toD less than or equal to 32 lattice spacings, for a choice of the surface field H-1 small enough that the dependence of H-c(D) on H-1 is still linear. It is shown that the results are consistent with the power laws predicted by Fisher and Nakanishi [M. E. Fisher and H. Nakanishi, J. Chem. Phys. 75, 5857 (1981)], namely T-c(infinity)-T-c(D)proportional toD(-1/nu), H-c(D)proportional toD(-(Delta-Delta1)/nu), where nu is the bulk correlation length exponent of the three-dimensional Ising model, and Delta, Delta (1) are the corresponding "gap exponents" associated with bulk and surface fields, respectively. As expected, the order parameter of the thin film near its critical point exhibits critical behavior compatible with the universality class of the two-dimensional Ising model. (C) 2001 American Institute of Physics.