Observed properties of thiol self-assembled monolayers (SAMs) on GaAs (001) surfaces can be explained by the presence of surface reconstructions, but their exact form is generally unknown. We propose a new approach to modeling the SAM-surface interface based on using alkanethiol dense packing structures as a starting point and adjusting the surface reconstruction to accommodate them. Obtained in such a way, model SAMs adsorb along the trenches in the [110] direction and exhibit a 19 degrees tilt and +/- 45 degrees twist angles, in agreement with available experimental data. The molecules of the SAM bind to both Ga and As, and cover only 50% of the available surface sites. The requirements for the SAM formation process to achieve the proposed structures are discussed.