This paper presents a numerical investigation using the two-parameter fracture mechanics approach for studying threaded fastener geometries. It was found that the constraint arising from the presence of a surface crack in a threaded fastener does influence the stress in the forward sector. Consequently, the actual stress field shows a deviation from the theoretical HRR solution. Implementation of the J-Q methodology provided an approach for approximating the threaded fastener stress state using a two-dimensional modified boundary layer representation. Results reveal the parameter Q to vary along the crack front and having lowest values at the free surface and peaking at the root of the crack. Lastly, it is shown that the magnitude of the parameter Q is influenced by the magnitude of loading, thereby increasing the dominance of the large-strain region.