A method for constant pressure Monte Carlo simulations in lattice gas models is described. The simulation box is placed between two hard walls with fluctuating distance, and periodic boundary conditions are applied in the perpendicular directions. Continuous volume fluctuations in the bounded direction are made possible by introducing a generalized volume, which interpolates between the discrete values that correspond to the given lattice. This is achieved by using a surface potential variable which makes the lattice surface layer next to the hard wall gradually less accessible to particle occupation. The method is applied to the equation of state of noninteracting lattice gas models, where exact results are available for comparison, and also to less trivial models of interacting point-particles and athermal lattice chains, for which the quasichemical approximation (QCA) provides reliable results to compare with. For the chain simulations the method can be used in conjunction with the configuration biased Monte Carlo procedure in order to enhance its performance However, since the Monte Carlo moves can be chosen to fit any desired kinetic model, our method can be used not only to generate constant pressure equilibrium ensembles, but also in the context of dynamic Monte Carlo studies. The center of mass diffusion in dense systems of athermal chains is investigated as an example. In all our static applications the method performs very well in comparison with exact or with QCA results, provided that the system size is large enough in the bounded direction. For small systems finite size effects are observed and analyzed, suggesting potential applications in the study of confined systems.