The behavior of headgroups in alkanethiol/Au(111) self-assembled monolayers (SAMs) is simulated using the Monte Carlo technique and a simple 2D model. The model treats the interaction of the alkane tails in an implicit way, in terms of an effective one-center potential describing the interaction of the sulfur headgroups. The form and parameters of the effective potential are chosen so as to mimic the intermolecular interactions in a decanethiol/Au(111) SAM. The interaction of the headgroups with the gold substrate is described by a surface corrugation potential of hexagonal symmetry. The phase and structural behavior of the model system is studied as a function of temperature, coverage, and the magnitude of surface corrugation. In addition to 2D melting, the model predicts a continuous commensurate-incommensurate solid phase transition, which involves the coexistence of commensurate and incommensurate regions. The simulation results provide a good starting point for subsequent studies of the role of the orientational and conformational degrees of freedom in the phase behavior of SAMs.