Pair interaction potentials have been developed by spline fitting cubic functions to reproduce perfect lattice properties. The lattice symmetry is taken as hcp with the rigid sphere c/a ratio and a cut-off distance between second and third neighbor is assumed. The lattice parameter, elastic constants and vacancy formation energy of Mg, Ti and Zr are consistently fitted by the potentials. We have calculated the lattice relaxation predicted by these potentials for the vacancy, and self interstitial in an otherwise perfect hcp lattice. The stability and dynamics of those defects are studied within the quasi-harmonic approximation. The interstitial site occupancy in hcp lattice and the vacancy and interstitial diffusion are discussed.