Multipath routing plays an important role in communication networks. It can increase the effective bandwidth between pairs of vertices, avoid congestion in a network and reduce the probability of dropped packets. In this paper, we built model for vertex-disjoint paths problem and then proposed algorithm for finding the shortest pair of vertex-disjoint paths. We consider in this paper the shortest-path problem in networks in which the length (or weight) of the edges are considered. We present algorithms for finding the shortest-path. In more restricted transit. Furthermore, we can extend this algorithm to find any k disjoint paths whose sum-weight is minimized.