Abstract: The materials with a set of penny-shaped cracks exhibited transversely radically isotropic. The Walpole’s base was introduced for tensorial represtation and calculation. The macroscopic stress states of the composites were defined by introducing the energy density supporting function. In order to capture the local deviatoric effects induced by a hydrostatic loading, the modified secant method based on energy approach was adopted in non-linear homogenized. Three schemes of macroscopic elastic moduli for microcracks materials were considered, i.e. dilute scheme, MT scheme and PCW scheme. It can be found from the research result that the elastic modulus ratios and the macroscopic friction coefficient tend to decrease with the increase of the crack volume fraction. The smaller the crack aspect ratio is, the larger of the difference is between the predictions by the dilute scheme, MT scheme and PCW scheme.