A three-dimension (3D) re-entrant honeycomb structure which exhibits negative Poisson’s ratio in all three principal directions is modeled from a classical two-dimension (2D) auxetic material. In this work, on the basis of the Castigliano’s second theorem and Timoshenko beam model, the shear deformation and axial deformation of this structure are investigated. And the analytical formulas of the effective modulus and Poisson’s ratio in each principal direction of the honeycomb structure are derived. By comparing the analytical results with the finite element analysis results, the rationality of the formula is verified. Then, the collapse characteristics of honeycomb structures with different mechanical properties under variation impact velocities are studied. The results show that, the deformation of honeycomb structure can be divided into three patterns, “quasi-static” deformation, “transitional” deformation and “local” deformation varied with impact velocities. And due to inertial effect, with the increase of impact velocity, the load-bearing capacity and energy absorption of the structure also increased. In addition to the impact velocity, the cells’ configuration is also a non-negligible factor, and its turns out that the decrease of angle accelerates the deformation state of the honeycomb structure and strengthen the energy-absorption capability after being subjected to impact load.