In this paper, two new 2D re-entrant topologies with negative Poisson's ratio are presented and their mechanical properties (Poisson's ratio and energy absorption capacity) are studied using finite element method as a function of geometric parameters. The first topology (model 1) was constructed by adding two sinusoidal-shaped ribs into the classical re-entrant topology, while the second topology (model 2) was made by introducing extra vertical ribs to reinforce the sinusoidal-shaped ribs. Simulation results show that model 1 and model 2 topologies can reach a minimum value in Poisson's ratio of - 1.12 and - 0.58 with an appropriate geometric aspect ratio, respectively. The energy absorption capacities of model 1, model 2 and classical re-entrant model were studied at various compression velocities. Enhanced energy absorption capacities were observed in the two new re-entrant topologies compared with the classical re-entrant topology. Model 2 exhibited the highest energy absorption capacity and a highest plateau stress. The plateau stress of model 1 was about half that of model 2, and when the compression velocity is more than 20 m/s, the plateau stress of model 1 became lower than that of the classical re-entrant model.