In this paper, we derive the general solutions for many cylindrical holes or rigid inclusions perfectly bonded to an elastic medium (matrix) of infinite extent, under In-Plane deformation. These many holes or rigid inclusions have different radii and different central points. The matrix is subjected to arbitrary loading like uniform stresses at infinity. The solution is obtained, via iterations of Möbius transformation as a series with an explicit general term involving the complex potential functions of the corresponding homogeneous problem. This procedure has been termed” heterogenization”. Using these solutions, several numerical examples are shown by graphical representation.