The paper describes the transverse shear properties of a novel centresymmetric honeycomb structure evaluated using analytical and Finite Element models. The cellular structure features a unit cell geometry allowing in-plane auxetic (negative Poisson’s ratio) deformations, and multiple geometry parameters to be used to design the honeycomb for multifunctional applications. The out-of-plane properties are calculated using a theoretical approach based on Voigt and Reuss bounds. The analytical models are validated using a full scale Finite Element technique to simulate transverse shear tests, a quarter FE unit cell with periodic shear conditions and an FE homogenisation method for periodic structures. The comparison between the analytical and numerical models shows good convergence between the different set of results, and highlights the specific deformation mechanism of the multi re-entrant honeycomb cell.