Ab initio calculations, based on pseudopotentials and the density functional theory, have been made to investigate the equilibrium atomic geometry, electronic states, and bonding of S adsorbates on the InP(110) surface with (1 X 1) periodicity. For nonreacted half-monolayer coverage of S, we find that the interchain bridging geometry has the lowest total energy. For nontreated full monolayer coverage the epitaxially continued layer structure is found to be the most energetically favorable, and exhibits a food semiconducting nature. We have also studied four geometrical models which involve a reaction of S atoms with the;substrate. For an ordered reacted model with the adsorbate S atoms exchanged with their neighboring P atoms, the average vertical distance between the top two layers is 1.98 Angstrom, which is in agreement with a recent result obtained from x-ray standing wave analysis, but is characterized by a small band gap.