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• Optimizing the inclined beams in re-entrant structural elements into buckling beams. • Improved structural element and negative Poisson's ratio metamaterial are designed. • The problem of stress concentration in structural elements is alleviated. • The negative Poisson's ratio characteristic of metamaterial is enhanced. Aiming at the problems of stress concentration and negative Poisson's ratio in the deformation process of the re-entrant structure, a cosine-shaped re-entrant structure negative Poisson's ratio metamaterial is proposed in this paper. By optimizing the inclined beams in the re-entrant structural elements into single cosine, tandem cosine and multiple cosine buckling beams, different configurations of improved re-entrant structural elements are designed. Finite element modeling and quasi-static compression simulations and experiments are carried out for single and periodically arranged re-entrant structures. The results show that the comprehensive stress of the single cosine structure and the tandem cosine structure are reduced by 18.7% and 58%, respectively, and the maximum stress can be reduced by 6.7% and 5.2%, respectively. In addition, the negative Poisson's ratio of metamaterial with a single cosine re-entrant structure is increased by 14% compared with that before the improvement. [ABSTRACT FROM AUTHOR]