In this paper, two classes of directed networks——ORC-networks and IRC-networks are defined, and a polynomial time algorithm is presented for computing their rooted communication reliability, i.e. the probability that a specified vertex, root vertex, can communicate with all other vertices. The complexity of the algorithm for ORC-networks and IRC-networks is O(｜E｜) and O(｜V｜·｜E｜) respectively, where ｜V｜ and ｜E｜ are the number of vertices and of edges of networks respectively.