The low in-plane modulus of honeycombs may be used for compliant structures with a high elastic limit while maintaining a required modulus. Numerical and finite element (FE) studies for a functional design of honeycombs having a high shear strength, (τpl *)12 and a high shear yield strain, (γpl *)12 are conducted with two material selections—mild-steel (MS) and polycarbonate (PC) and five honeycomb configurations, when they are designed to be a target shear modulus, G12 * of 6.5 MPa. A numerical study of cellular materials theory is used to explore the elastic limit of honeycombs. FE analysis is also employed to validate the numerical study. Cell wall thicknesses are found for each material to reach the target G12 * for available cell heights with five honeycomb configurations. Both MS and PC honeycombs can be tailored to have the G12 * of 6.5 MPa with 0.1–0.5 mm and 0.3–2.2 mm cell wall thicknesses, respectively, depending on the number of vertical stacks, N. The PC auxetic honeycomb with θ= −20 deg shows high shear flexibility, when honeycombs are designed to be the of 6.5 MPa; a 0.72 MPa (τpl *)12 and a 13% (γpl *)12 . The authors demonstrate a functional design with cellular materials with a large design space through the control of both material and geometry to generate a shear flexible property.