•An analytical model was established and analyzed for the first time.•The design was verified with experiments and finite element analysis.•The tailorability of mechanical properties was demonstrated for the structure.•Manufacturing induced mechanical property issues were discussed. In this work, an analytical model of a 3D re-entrant honeycomb auxetic cellular structure has been established based on both a large deflection beam model and a Timoshenko beam model. Analytical solutions for the modulus, Poisson’s ratios and yield strength of the cellular structure in all principal directions were obtained, which indicate a wide range of mechanical property control via geometrical designs. The results were compared with experimentation and finite element analysis, and it was verified that the analytical model provides a convenient and relatively accurate method in the prediction of the performance for the auxetic cellular structures once the manufacturing related factors are adequately incorporated into the model. It was also found that the model provides less accurate predictions when higher-order coupling effects such as warp locking becomes significant under lower structural symmetry.