The present invention relates to an axisymmetric chiral auxetic structure. The invention belongs to the field of materials design. The invention is an axisymmetric chiral cellular structure with a cylindrical or spherical shape consisting of equal or variable unit chiral cells. The structure exhibits auxetic deformation behaviour with negative Poisson’s ratio in all polar or spherical coordinate directions upon mechanical loading. The deformation of the cylindrical chiral auxetic structure is isotropic in the radial direction under axial loading.