A re-entrant chiral auxetic (RCA) structure is a new structure, which comprises three topologies: re-entrant, trichiral and anti-trichiral. The aim of this study is to numerically investigate the influences of geometrical parameters of a RCA unit cell on the in-plane tensile properties. Finite element (FE) models were developed using commercial software, ABAQUS 6.11–2, and verified by experimental results. Based on the verified FE models, a parametric study was performed to examine the effects of geometrical parameters on the stress–strain curve and Poisson’s ratio of a RCA structure. In order to reduce the variables studied, three dimensionless groups of geometrical parameters were proposed. Results showed that the RCA structure predominantly deformed by bending and stretching of walls as well as rotation of cylinders. The RCA structure displayed high stress, low strain and large negative Poisson’s ratio when it was loaded in the X direction. On the other hand, the RCA structure exhibited low stress, high strain and a transition from negative to positive Poisson’s ratio when it was loaded in the Y direction. The geometrical parameters of the RCA structure had significant effects on its stress–strain curves and Poisson’s ratios. The findings of this study provide an insight into the mechanical response of the RCA structure under uniaixal tensile loading.