||Cellular solids, including cellular materials and cellular structures (CMS), have attracted people's great interests because of their low densities and novel physical, mechanical, thermal, electrical and acoustic properties. They offer potential for lightweight structures, energy absorption, thermal management, etc. Therefore, the studies of cellular solids have become one of the hottest research fields nowadays. From energy absorption point of view, any plastically deformed structures can be divided into two types (called type I and type II), and the basic cells of the CMS may take the configurations of these two types of structures. Accordingly, separated discussions are presented in this thesis. First, a modified 1-D model is proposed and numerically solved for a typical type II structure. Good agreement is achieved with the previous experimental data, hence the model is used to simulate the dynamic behavior of a type II chain. Resulted from different load speeds, interesting collapse modes are observed, and the parameters which govern the cell's post-collapse behavior are identified through a comprehensive non-dimensional analysis on general cellular chains. Secondly, the MHS specimens are chosen as an example of type I foam materials because of their good uniformity of the cell geometry. An extensive experimental study was carried out, where more attention was paid to their responses to dynamic loadings. Great enhancement of the stress-strain curve was observed in dynamic cases, and the energy absorption capacity is found to be several times higher than that of the commercial metal foams. Based on the experimental study, finite elemental simulations and theoretical modeling are also conducted, achieving good agreements and demonstrating the validities of those models. It is believed that the experimental, numerical and analytical results obtained in the present study will certainly deepen the understanding of the unsolved fundamental issues on the mechanical behavior of cellular solids and make substantial contributions to the theoretical advance of impact dynamics.