Yttrium hydride (YH2) is of interest as a high temperature moderator material because of its superior ability to retain hydrogen at elevated temperatures. Thermal neutron scattering laws for hydrogen bound in yttrium hydride (H-YH2) and yttrium bound in yttrium hydride (Y-YH2) prepared using the ab initio approach are presented. Density functional theory, incorporating the generalized gradient approximation (GGA) for the exchange-correlation energy, is used to simulate the face-centered cubic structure of YH2 and calculate the interatomic Hellmann-Feynman forces for a 2 × 2 × 2 supercell containing 96 atoms. Lattice dynamics calculations using PHONON are then used to determine the phonon dispersion relations and density of states. The calculated phonon density of states for H and Y in YH2 are used to prepare H-YH2 and Y-YH2 thermal scattering laws using the LEAPR module of NJOY2012. Analysis of the resulting integral and differential scattering cross sections demonstrates adequate resolution of the S(α,β) function. Comparison of experimental lattice constant, heat capacity, inelastic neutron scattering spectra and total scattering cross section measurements to calculated values are used to validate the thermal scattering laws.