Abstract: In this paper, a cylinder torsion model and a torsion energy method are proposed to predict equivalent outplane shear modulus of hexagon cellular materials. An analytical expression for its size effect is constructed in terms of volume fraction(ν), number of cells in circumference(n), radius of the hollow cylinder(r) and number parameter of cell layers(m). Comparisons are made among the results of torsion energy method, finite element numerical simulation and G-A microstructure mechanical method. The size effect is revealed and proved theoretically. Numerical results show that when the cell size trends to be infinitely small with regard to the size of the structure, predicted results approach those obtained by mesoscopic mechanics method. Due to the cyclic symmetry of periodic cellular materials, it is shown that the computing efficiency can be greatly increased by means of the substructure model.