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In this current work, a Ti–6Al–4V 3-D re-entrant lattice auxetic structure is manufactured by the electron beam melting (EBM) process. Four different design configurations (two negative Poisson’s ratio values×two relative densities) were manufactured and tested under compressive stress. Two failure modes were observed whose occurrence appeared to be dependent on the ratio of vertical strut length to re-entrant strut length. A small deflection analytical model is presented that predicts yield strength and modulus for one type of design with good accuracy. Results also show that the re-entrant lattice structure possesses superior mechanical properties compared to regular foam structures. Limitations of the analytical model are also discussed.