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The present work deals with the modeling of multi-defected solids under the action of large deformation. A micromechanics constitutive model, formulated in terms of the compressible anisotropic NeoHookean strain energy density function, is presented to characterize the corresponding nonlinear effective elastic behavior. By employing a scalar energy parameter, a correspondence relation between the effective hyperelastic model and this energy parameter is established. The corresponding effective material coefficients are then evaluated through combined use of the “direct difference approach” and the extended “modified compliance contribution tensor” method. The proposed material constitutive model can be further used to estimate the effective mechanical properties for engineering structures with complicated geometry and mechanics and appears to be an efficient computational homogenization tool in practice.