Using first-principles total energy calculations, we investigate the structural stability and electronic properties of Re3ZnNx (x = 0, 0.25, 0.5, 1) and Re3ZnX (X = H, B, C, and O) compounds. The calculations indicated that interstitial atoms including N, H, B, C, and O, always prefer the octahedral sites to the tetrahedral sites in the studied hexagonal structure, in good agreement with the experimental results. However, the calculated heat of formation and elastic properties suggest that the incorporation of nitrogen is not favorable for the formation of the Re–Zn alloy, but high pressure and high temperature lower the energy barrier to facilitate the incorporation of N into Re3Zn alloy. Furthermore, B addition displays the highest effect in strengthening Re–Zn alloy upon the formation of relatively-strong boron–boron bond and thus higher shear modulus. Also, the ductile character of these alloys is important for possible applications.