Fluorination of a dimerized Si(001)-2x1 surface near single-layer high step edges has been studied with molecular statics and dynamics simulations using the Stillinger-Weber potential for Si-Si, Si-F, and F-F interactions. Binding energies for up to three F atoms on Si atoms at the step edges have been investigated for fully relaxed; systems. We find that F-bonded Si atoms relax away from the surface with increasing fluorination which lowers the desorption/etching energies of SiFx(x = 1,3) species. Room temperature molecular dynamics simulations then show direct etching of SiF3 from Si atoms bonded to step edges. The calculations predict an anisotropy in the step edge induced etching of the Si(001)-2x1 surface. This is in qualitative agreement with an experimental observation on the same surface though using Cl instead of F atoms.