The modified embedded-atom method, MEAM for hcp Mg & Ti metals and alloys have been designed. The monovacancy formation, migration and activation energies in the hcp out plane were computed and reasonably agree with available data from experiments. The divacancy formation and binding energies of the first nearest-neighbour were reported. The computed value for the binding energy is positive, an indication of stability. The five independent elastic constants in hcp metals were determined and they all correlate with the experimental values. Finally, the enthalpy of solution for Mg(H)Ti(G) and Mg(G)Ti(H) binary alloys were considered. The values are positive but data from experiment are unavailable. For a better comparism, data from experiment are seriously needed.