In the analysis of materials containing regularly placed in-homogeneities, the evaluation of homogenized properties is an important issue. Common procedure for the homogenization is to define a unit cell, load it somehow, and investigate its structural response. A periodic variation of strain appears when the periodically heterogeneous material is under uniform macro-stress, and therefore, the implementation of this characteristic behavior would be essential to the material characterization based on a unit cell analysis. With the method proposed here, conventional finite element analysis tools can be used with no modification, and it is applicable to the skew-arrayed in-homogeneity problems. The orthotropic elastic and creep properties of materials with voids are examined, and the accuracy and effectiveness are demonstrated.