The growing demand for tyres in transport industry provides a negative impact on the environment, due to the problems related to recycling and disposal of the rubber waste. However, adding waste tyres as a dispersive phase in polymeric composites has shown high toughness and moderate increase of mechanical strength within the composites. In this work, we investigate the use of recycled rubber core to manufacture auxetic (re-entrant) honeycomb structures. The re-entarnt honeycombs produced are evaluated using finite element analysis and tensile in-plane to assess the sensitivity of the mechanical properties versus the cell geometric parameters. A full factorial design (33) was performed to investigate the effects of the factors width (10 and 20 mm), thickness (2 and 4 mm) and angle (−10 and −20°) on Poisson's ratio of honeycomb structures. The results give further evidence that the Poisson's ratio is affected not only by individual factors but also by interaction originated by the other geometric parameters.