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Cellular materials' two important properties—structure and mechanism—can be selectively used for materials design; in particular, they are used to determine the modulus and yield strain. The objective of this study is to gain a better understanding of these two properties and to explore the synthesis of compliant cellular materials (CCMs) with compliant porous structures (CPSs) generated from modified hexagonal honeycombs. An in-plane constitutive CCM model with CPSs of elliptical holes is constructed using the strain energy method, which uses the deformation of hinges around holes and the rotation of links. A finite element (FE) based simulation is conducted to validate the analytical model. The moduli and yield strains of the CCMs with an aluminum alloy are about 4.42 GPa and 0.57% in one direction and about 2.14 MPa and 20.9% in the other direction. CCMs have extremely high positive and negative Poisson's ratios (NPRs) ($νxy*$ ∼ $±40$) due to the large rotation of the link member in the transverse direction caused by an input displacement in the longitudinal direction. A parametric study of CCMs with varying flexure hinge geometries using different porous shapes shows that the hinge shape can control the yield strength and strain but does not affect Poisson's ratio which is mainly influenced by rotation of the link members. The synthesized CPSs can also be used to design a new CCM with a Poisson's ratio of zero using a puzzle-piece CPS assembly. This paper demonstrates that compliant mesostructures can be used for next generation materials design in tailoring mechanical properties such as moduli, strength, strain, and Poisson's ratios.