This paper presents a numerical study of regular and hierarchical honeycomb structures subjected to out-of-plane impact loading. The specific energy absorption capacity of honeycomb structures via nonlinear explicit finite element analysis is investigated. The constructed finite element models are validated using experimental data available in the literature. The honeycomb structures are optimized by using a surrogate-based optimization approach to achieve maximum specific energy absorption capacity. Three surrogate models polynomial response surface approximations, radial basis functions, and Kriging models are used; Kriging models are found to be the most accurate. The optimum specific energy absorption value obtained for hierarchical honeycomb structures is found to be 148% greater than that of regular honeycomb structures.