The formal solution resulting from the scattering of a plane, time-harmonic, compressional elastic wave impinged on a group of parallel circular cylindrical inclusions in a finite domain is obtained. The inclusions are rigid as well as immovable and the geometry of their configuration is arbitrary. The technique of “multiple scattering” which was developed in acoustic and electromagnetic wave propagation is applied. The stress field around two identical circular cylindrical inclusions at a finite separation is studied in detail.