We report the results of theoretical studies on the self-assembled monolayers of benzenethiolate (BT) and benzyl mercaptide (BZM)on a Au(111) surface. A few relevant potential energy parameters were determined. We have performed annealing type molecular dynamics simulations where the minimized initial configurations are heated to 1000 K and then cooled to room temperature, assuming two types of unit cells: root 3 x root 3R30 degrees and 2 x 2. The results of the simulations showed that BZM formed a nearly perfect herringbone structure, while the apparent herringbone type structure of BT was somewhat disordered in the root 3 x root 3R30 degrees unit cell. For the 2 x 2 unit cell with larger area per molecule, both monolayers did not form well-ordered structures, but the BZM showed some local ordering with herringbone structure. In both cases, the molecules of BZM are found to be nearly vertical to the surface, while those of BT are tilted from the surface normal. All these theoretical results are consistent with recent experimental findings. The role of a flexible methylene unit near the sulfur headgroup in discriminating stable packing structures of the self-assembled monolayers is discussed.