A re-entrant honeycomb structure made from a novel solid composite based on recycled rubber is an innovative and sustainable solution for engineering applications. This work describes the tensile and failure behaviour of multi re-entrant honeycomb topologies consisting of width, thickness and angle variations. Finite element (FE) models were also developed to simulate tensile tests and failure behaviour of the cellular structures. A Taguchi design (L8) was conducted to determine the effect of each factor on the ultimate strength, ultimate strain, modulus of elasticity, Poisson's ratio and Von Mises stress. The experimental and FE results showed a good correlation, validating the numerical model which was used to perform a parametric analysis on the influence of the cell geometry over the failure behaviour of the structures. The magnitude of Poisson's ratio was significantly affected by the level of each cell geometric parameter. The structures with lower Poisson's ratio values were able to absorb more energy, and consequently, exhibiting less points of failure. It was found the thickness and the width has a significant effect on the tensile properties and failure behaviour.