We study ordering within closely packed monolayers of thiol derivatives self-assembled on gold substrates by chemisorption from solution. We discuss constant stress molecular mechanics and dynamics simulations of alkanethiolate monolayers on Au(111) and Au(100) surfaces. In the first case, we use the MM2 force field augmented with classical chemisorption parameters obtained from fitting to results of ab initio quantum mechanical calculations. In the second, the chemisorption to the Au(100) surface was accomplished by using harmonic constraints to restrict the thiolate groups to the square lattice. It is shown that two chemisorption modes of alkanethiolate on Au(111) exist, and that both give closely packed ordered monolayers. In the system on Au(100), rearrangement towards close-packing is achieved at the expense of distortions that increase the intrachain elastic energy.