The in-plane compressive collapse and fracture toughness of a hierarchical hexagonal honeycomb with sandwich walls consisting of corrugated cores are studied by using finite element method. Its near-optimal configuration is identified by maximizing its elastic limit, which is determined by three competing failure modes including plastic yielding of the larger struts, or elastic wrinkling of the face sheets of the larger struts, or elastic buckling of the smaller struts. The overall mechanical properties of the optimal hierarchical honeycomb, including the Young’s modulus, elastic limit, peak strength, and fracture toughness are obtained from finite element method simulation and compared with analytical predictions, and the discrepancy between the two is explained. The optimal hierarchical honeycomb is found to be superior to its equivalent mass first-order honeycomb in all the mechanical properties listed above when the relative density is low (about 10%). Moreover, the Young’s modulus, elastic limit and peak strength under plastic failure mode, and the fracture toughness of this optimal hierarchical honeycomb are shown to depend linearly upon its relative density. This paper provides additional insights into hierarchical cellular materials.