A simple two-site molecular model is suggested for computer simulation of self-assembled monolayers (SAMs) formed by long-chain functionalized molecules on the surface of solid substrates. In this model, one force site, placed at the functional headgroup, is responsible for the interaction of the headgroup with the periodic substrate field and the other headgroups. The second force site, positioned in the middle of the molecule, describes the chain-substrate and chain-chain interactions. For the latter interaction, a Gay-Berne-Pechukas orientation-dependent potential is used. The parameters of the model potentials are chosen so as to mimic the interactions in alkanethiol/Au(111) SAMs. The phase and structural behavior of the model system is explored using the Monte Carlo technique as a function of temperature, coverage, and the magnitude of surface corrugation. Simulations reveal a commensurate-incommensurate solid-phase transition preceding two-dimensional melting. At incomplete coverages, a two-phase region is observed, in which the usual crystalline phase characteristic of saturation coverage coexists with a low-density translationally disordered phase. The surface-aligned "striped" phase observed in STM experiments [G. E. Poirier and E. D. Pylant, Science 272, 1154 (1996)] can only be modeled at low temperatures assuming head-to-head dimerization of the molecules.