This paper investigates the combined effects of relative density and material distribution on the elastic constants and the yield strength of metallic honeycombs. Periodic regular hexagonal cell is employed as the structural model. Bending, transverse shearing and axial stretching (or compression) are taken into account in the analysis. Closed-form solutions for the yield strength and for all the five independent elastic constants are obtained for honeycombs with cell walls of uniform thickness. For honeycombs with cell walls of non-uniform thickness, the closed-form solutions would be too lengthy to use in practical applications. We instead provide the numerical results to show the combined effects of relative density and material distribution on the yield strength and on all the five independent elastic constants of metallic honeycombs. The results can serve as a guidance for the optimal design of metallic honeycombs.