We describe a study of the Si(001) surface structure using 0.1 - 2.0 MeV He+ ion scattering. The experimental configuration required for this work is discussed in detail. The measured intensities of the Si surface peak as a function of energy are presented for the clean Si(001) surface and two different states of the hydrogen covered Si(001) surface. The hydrogen (deuterium) coverage is determined via the 3He(d, p)4He reaction. The experimental results are compared to computer simulations; various aspects of the model of thermal vibrations used in the simulation are discussed. The results indicate that there is extensive sub-surface stain in the reconstructed Si(001) surface.