We report grand canonical Monte Carlo simulations for a Lennard-Jones (LJ) fluid modelled on methane in slit-shaped pores of several materials and pore widths. Three types of pore wall were considered : graphitic carbon (strongly attractive walls),"methane" walls (wall attractions equal to those in the adsorbate phase), and hard walls. For each system the change from a fluidlike to a solidlike adsorbed phase was observed, and the shift in freezing or melting temperature from that of the bulk adsorbate material was determined. As well as changes in the overall properties of the adsorbate phase, corresponding changes in the individual adsorbate layers in the pore were studied. In addition hysteresis on heating and cooling was examined. For the graphitic carbon walls the freezing temperature was raised relative to that of the bulk material, the elevation being greater for smaller pore widths; however, no freezing transition was observed for pore widths below about 5.3a. In addition, the contact layer of adsorbate froze at a temperature higher than the inner layers. For pores with methane walls (walls of LJ molecules having the same density and intermolecular interactions as the adsorbate phase) no shift in freezing temperature occurred, while pores with hard walls showed a decrease in freezing temperature relative to the bulk; in the case of hard walls, the contact layer of adsorbate froze at a lower temperature than the inner layers. Considerable hysteresis was observed in some cases, and the width of the hysteresis loop was sensitive to pore size, being wider for pores in which the adsorbed layers are tightly packed. The results indicate that the direction and magnitude of the shift in freezing temperature in the pore is strongly dependent on the strength of the attractive forces between the adsorbate molecules and the wall, and particularly on the magnitude of this relative to Such forces between the adsorbate and a wall composed of the same adsorbate molecules. A simple thermodynamic model based on this idea is proposed, and showed to give a good account of the simulation results for methane in carbons. In the simple systems studied here the confinement causes little change in the solid lattice structure of the bulk material. This is unlikely to be the case for more complex pore geometries, and the analysis of such cases is likely to involve additional structural effects.