In this paper, tunneling effect of Cooper pairs in weak-link superconductor structure with multi-junctions under the condition for overstepping the Josephson approximation is discussed. The equations describing the electric current based on the tunneling effect of Cooper pairs in several kinds of weak-link superconductor structures with multi-junctions are obtained under the condition to overstep the Josephson approximation. For both SISISIS and a four junctions ring, when all junctions are in the zero voltage state, the exact solution of the equations is obtained. It is found that, because of...