The density functional theory (DFT) is used to study the atomic interactions in transition metal-based interstitial alloys. The strain field is calculated in the discrete lattice model using Kanzaki method. The total energy and hence atomic forces between interstitial hydrogen and transition metal hosts are calculated using DFT. The norm-conserving pseudopotentials for H, Cu and Pd are generated self-consistently. The dynamical matrices are evaluated considering interaction up to first nearest neighbors whereas impurity-induced forces are calculated with M₃₂H shell (where M = Cu and Pd). The atomic displacements produced by interstitial hydrogen at the octahedral site in Cu and Pd show displacements of $7.36$% and $4.3$% of the first nearest neighbors respectively. Both Cu and Pd lattices show lattice expansion due to the presence of hydrogen and the obtained average lattice expansion $\Delta V /V = 0.177$ for Cu and 0.145 for Pd.