In this paper, we present an algorithm for the multicast routing problem when there exit the cell replication limits of ATM switching nodes. This problem can be formulated as a Degree Constrained Minimum Steiner Tree Problem(DCSP). The proposed algorithm is a modification of the shortest path heuristic originally devised for minimum Steiner tree problem. From the experimental results, it can be seen that our algorithm is efficient to obtain a near optimal solution with comparatively low computational time.