Cellular materials with negative Poisson’s ratio have unique mechanical performance and a promising prospect of applications. A mechanical model of two-dimensional cellular materials with negative Poisson’s ratio, composed of partly re-entrant and partly regular hexagons, was proposed based on rotation mechanism. The relationships of both Poisson’s ratio and sitiffness coefficients with the angles were predicted. The shear strain of the model was obtained. Energy method was used to develop the elastic constitutive equations. Results show that the mechanical model gave rise to not only a negative Poisson’s ratio, but also a positive one greater than 1 and performed a characteristic of negative stiffness. The stiffness coefficients of the model could be altered by adjusting the ratio of the cell ribs length and the characteristic angle. The results are useful for designing the microstructures of two-dimensional cellular materials.