We investigate the normal impact of a rigid sphere on a half-space of elasto-plastic auxetic/metal foam using the finite element method. The dependence of the coefficient of restitution, peak force, maximum displacement, and contact duration on the yield strain, impact velocity, and elastic and plastic Poisson’s ratio is analyzed. For a given elastic Poisson’s ratio, the coefficient of restitution generally decreases with an increase in the plastic Poisson’s ratio and impact velocity. When the plastic Poisson’s is maintained constant, the coefficient of restitution increases with an increase of the elastic Poisson’s ratio. These trends are explained using plastic energy dissipation. The energy dissipation trends are further investigated by decomposing it into deviatoric and hydrostatic parts. For a given impact velocity, the peak force is relatively insensitive to most of the elastic and plastic Poisson’s ratio combinations. We also show that for the cases where the elastic and plastic Poisson’s ratios are equal, the coefficient of restitution is relatively insensitive to their actual values. These findings can guide researchers to identify the right elastic and plastic Poisson’s ratio combinations so that lattice materials with exceptional energy absorbing capacity can be designed using topology optimization.