First-principles calculations on neutral metal impurities (Mg,Zn and Ca) in zinc blende GaN were studied. Formation energies were calculated for substitution on the gallium site,the nitrogen site and incorporation in the octahedral interstitial site and the tetrahedral interstitial sites. The calculated results show that the major defects studied have a high formation energy in excess of 5 eV,and the gallium substitutional site is favorable for incorporation. MgGa has particularly low formation energy 1.19 eV and can be expected to incorporate readily into GaN. The local crystal structural changes around the impurity in the lattice were studied after metal atoms occupying the gallium substitutional site. It shows that the lattice constant becomes bigger and the tetrahedral angle between impurities and its nearest N atom becomes smaller mainly due to the extended M-N bond length and big size of impurities atoms,which results in a local lattice distortion. The Zn-N (2.04 (A)) bond strength is the smallest among the three impurities which raises the formation energy. CaGa is unfavorable due to a large size mismatch in spite of a large bond strength (2.25 (A)). The calculated results identify the two key factors determining impurities incorporation in zinc blende GaN: the atomic size of impurities comparing to that of host atoms and the bond strength between the impurities and its neighbors. The results are in well agreement with other calculated and experimental results.