The elasto-plastic indentation of auxetic and metal foams is investigated using the finite element method. The contributions of yield strain, elastic, and plastic Poisson's ratio on the indentation hardness are identified. For a given yield strain, when the plastic Poisson's ratio is reduced from 0.5, the indentation hardness decreases first and then increases. This trend was found to be valid for a wide of yield strains. For yield strains less than 0.08, the hardness of auxetic materials is much larger when compared with materials having positive plastic Poisson's ratio. As the plastic Poisson's ratio approaches-1, the elastic deformations dominate over the plastic deformations. The plastic dissipation, when compared with the elastic work, is lower for materials with negative Poisson's ratio. There is no effect of elastic Poisson's ratio on the indentation hardness when the plastic Poisson's ratio is more than-0.8. When the plastic Poisson's ratio is less than-0.8, the hardness increases with a decrease of elastic Poisson's ratio. The plastic dissipation per unit strain energy is maximum for materials with vanishing plastic Poisson's ratio. © 2021 by ASME.