An epitaxial $eta-FeSi_2$ structure on Si (001) substrate was calculated by using density functional theory (DFT). Unit cell of orthorhombic $eta-FeSi_2$ and $sqrt{2} imessqrt{2} imes2$ supercell were calculated to find the energetically favorable structures first. The $chi$- and y-direction axes of $eta-FeSi_2$ were changed into y- and z-direction axes to match its structure with that of Si, to minimize the lattice mismatch between $eta-FeSi_2$ and Si. Distance between the Si (001) surface and the $eta-FeSi_2$ surface was varied to find an optimum distance between them, resulting in 0.825 $AA$.