This paper presents the use of elastic metamaterials for impact attenuation and blast-wave mitigation. Metamaterials represent a novel and emerging research area where materials exhibit exceptional properties not commonly found in natural materials. These unique properties are enacted by specifically designed microstructures. In this study, a single-resonator model and a dual-resonator microstructural design are proposed to exhibit negative effective mass density. The effect of negative effective mass density is explicitly confirmed by analysis of wave propagation using numerical simulations. Results evidently show that impact stress wave attenuation occurs over a wider frequency spectrum for the dual-resonator model as compared to the narrow band gap of a single-resonator design. Parametric studies of blast-wave simulation reveal that the mass and number of internal resonators have significant influence over the frequency range of blast-wave attenuation. The effectiveness and performance of the single-resonator and dual-resonator models on blast-wave mitigation are examined and discussed. Finally, practical ways to design and manufacture elastic metamaterials with negative effective mass density are presented and explored.