Monte Carlo calculations have been used to study the mechanical relaxation of a monolayer of CH₃(CH₂)₁₅SH admolecules on a gold substrate when subjected to indentation caused by a nanometer-scale force-microscope tip. An almost elastic response is observed to forces that compress the monolayer by about 25% of its original thickness. Jump to contact on approach of the tip is signaled by an abrupt change in the mean molecular tilt, and the subsequent compression leads to very substantial but reversible changes in the conformations of the molecules. Comparison is made with results obtained by interfacial-force microscopy.