Tetragonal-$Ni_{1-x}Pd_x$Si/Si (001) structure was studied by using density functional theory (DFT). An epitaxial interface between $2{ imes}2{ imes}4$ (001) tetragonal-NiSi supercell and $1{ imes}1{ imes}2$ (001) Si supercell was first constructed by adjusting the lattice parameters of B2-NiSi structure to match those of the Si structure. We chose Ni atoms as a terminating layer of the B2-NiSi; the equilibrium gap between the tetragonal-NiSi and Si was calculated to be 1.1 ${AA}$. The Ni atoms in the structure moved away from the original positions along the z-direction in a systematic way during the energy minimization. Two different Ni sites were identified at the interface and the bulk, respectively. The two Ni sites at the interface have 6 and 7 coordination numbers. The Ni sites with coordination number 6 at the interface were located farther away from the interface, and were more favorable for Pd substitution.