Cellular structures having negative Poisson’s ratios can be designed to have high shear flexure properties. In this paper, the elastic limits of hexagonal honeycombs including the ones having negative Poisson’s ratios (NPR) are explored with various cell geometries under simple shear loading. While designing a shear modulus, e.g., G 12 ∗ of 10 MPa, of hexagonal honeycombs, corresponding meso-structures are designed with three constituent materials; an aluminum alloy (7075-T6), a titanium alloy (Ti–6Al–4V), and a high strength steel (ANSI 4340). The in-plane linear elastic honeycomb model is employed to achieve the shear moduli of the hexagonal honeycombs made of the three constituent materials. The shear strengths, ( τ pl ∗ ) 12 and shear yield strains, ( γ pl ∗ ) 12 of hexagonal honeycombs are obtained from finite element analysis using ABAQUS. The titanium alloy honeycombs show a good shear flexure property having both high ( τ pl ∗ ) 12 and ( γ pl ∗ ) 12 when it is designed to the target G 12 ∗ . The re-entrant geometry makes honeycombs flexible associated with a high effective bending length.