Abstract: This work attempts to find a new homogenization method for the analysis of assemblage of elastic contact bodies. A brief review of existing works for both micro or local analysis level and macro analysis level of the problem is given. The finite element method for the local RVE analysis is presented. An important feature of this work is the quasi-static cohesive frictional contact analysis of RVE, i.e. the local composed of deformable elastic bodies, by means of the parametric quadratic programming principle and its corresponding algorithmic implementation. The work presented in this paper is a fundamental study for the homogenization analysis of the problem.