Various local variations of the material microstructures lead mesoscale homogenization techniques considering capability in computer analysis. In this study moving window generalized method of cells technique is used to capture small scale material heterogeneity and randomness. Elastic and inelastic behavior considering yield criterion of plasticity are investigated. This mesoscale representation regarding the material constitutive models described is implemented into the finite-element model to which loading will be applied, is considered the macroscale model. Numerical simulations are demonstrated through comprehensive comparison with the examples in the literature.