Canonical Monte Carlo simulations were used to study the adsorption and compression of fluid layers on model substrates with cubic, (111) fcc, and graphite geometries. The effect of the relative size of the fluid and substrate molecules on adsorption was considered for strong molecule-surface interactions. In the case of monolayer formation, it was found that the surface geometry and the size of the adsorbate molecules had a significant effect on the structure of the adsorbed layer. These structures varied from well-ordered, commensurate layers to liquid-like structures. Lateral compression was observed for certain fluid to substrate molecule sizes. For the interactions studied in this work, it was found that maximum lateral compression occurred on the cubic surface when adsorbate molecules had a diameter approximately 15% larger than the substrate diameter. In the case of multilayer formation, it was found that second and higher adsorbed layers could compress into the adsorbed layers below them. For cubic substrates, the interlayer compression was predicted analytically with reasonable accuracy, with maximum interlayer compression found for fluid diameters approximately 90% the size of substrate molecule diameters. (C) 2004 American Institute of Physics.