Periodic lattice structures as lightweight and high-energy absorption materials have been widely used in various fields, among which re-entrant and Kelvin cell lattice structures have exhibited excellent mechanical behaviors under different loadings. Therefore, this study aims to numerically explore and compare the tensile mechanical responses of re-entrant and Kelvin cell lattice structures with the same relative density after validating with experimental tests. It has been found that the tensile behavior of the two stretching-dominated lattice structures resemble that of parent solid material but had smaller fracture stress and strain due to the lower ductility of the lattice structures. The re-entrant lattice structure displayed a better energy absorption capacity than the Kelvin cell lattice under tensile loading, i.e., the energy absorption and specific energy absorption of the re-entrant lattice were 3 times and 1.6 times, respectively, those of the Kelvin cell lattice. Meanwhile, the re-entrant lattice as expected exhibited auxetic behavior with a negative Poisson’s ratio during the whole stretching process, while the Kelvin cell had the mechanical behaviors of traditional materials with a relatively constant positive Poisson’s ratio. These results are expected to provide hints on mechanical references and guidance for their extensive applications in the future.