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Mechanical metamaterials offer unique possibilities to tune their mechanical response by adjusting their geometry, without the complexity that the thermodynamics and kinetics of materials synthesis otherwise impose. In this work, the tuning of the quasi-static and wave propagation properties of micro-lattice structures are explored using numerical methods. The ability to independently modify the elastic moduli and the dispersion properties of the material by appropriately placing micro-inertia elements is demonstrated. The numerical methods used for this investigation are also presented.