A comprehensive theoretical study is presented of the adsorption mechanism and energetics of the silyl (SiH3) radical on the Si(001)-(2 x 1) surface terminated by one monolayer of hydrogen atoms. SiH3 adsorbs on the surface dissociatively through an insertion reaction that involves breaking of the Si-Si surface dimer bond and subsequent transfer of an H atom from the radical to an atom of the broken dimer, thus leading to formation of two surface dihydride (SiH2) species. The structure and energies of the corresponding equilibrium and transition-state configurations are presented, as well as detailed energetics along the reaction pathway.