Using the finite element method, we investigate the elasto-plastic impact of a rigid sphere on a half-space of auxetic and metal foams. The validity of the Hertz theory for elastic impacts is investigated for both positive and negative Poisson’s ratio. For elastic impacts, the results from Hertz theory are accurate within 20 % with the finite element simulations. The plasticity is modeled using the Deshpande-Fleck metal foam yield criterion. This yield criterion allows for plastic compressibility and can also accommodate materials having a negative Poisson’s ratio. The elasto-plastic simulations reveal that the coefficient of restitution decreases as the impact velocity is increased. The coefficient of restitution is also least for materials having a zero plastic Poisson’s ratio. Our study suggests for maximum energy dissipation the plastic Poisson’s ratio should be close to zero. © 2019 Nitish Kumar, et al.