This paper is devoted to study of the limiting behaviour of an elastic material with periodically distributed rigid inclusions of size ε, as the small parameter ε goes to zero. We address here the case with inclusions of the same size as the period of the structure. The body in consideration here is suppose to be clamped on one part of its exterior boundary and submitted to given tractions on the other. By means of the well known two-scale convergence techniques, one convergence result is proved.