This lecture is connected with a pioneering work of . Jean and P. Breitkopf on the use of the parallel computing for the granular dynamics [1]. The chosen parallel strategy is similar to a Domain Decomposition Method (DDM), even if the substructuring procedure is more modestly called a "box method" and does not refer explicitly to a DDM. The Domain Decomposition methods in the context of multiprocessor computations, are well established from theoretical and practical standpoints when dealing with a linear system derived from a discretization of a continuous problem [4].