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It is still a technique "bottleneck" for continuous development of the city rail transit that how to determine the transfer paths made by passengers and how to implement clearing transfer transactions and ticket revenues in the city rail transit network in which the "transfer with one ticket in station" would be implemented. In this paper, a simplified modeling algorithm of rail transit network has been studied, which is implemented in terms of the network topology graphs of 8 lines operating in Shanghai rail transit now. The situation of repairing overlap edges and identifying edges with common stations is considered in the algorithm. Some idea for quick searching of 2nd or 3rd shortest path deviated from 1st or 1st and 2nd shortest paths, and a method for replacing back of keyless nodes in the modeling algorithm are presented, as well. We also study the searching algorithm for three shortest paths with the application methods in terms of its output results of city rail transit network implemented "transfer with one ticket in station" in the article. It is possible to extend some of our ideas to the system with Kth(>3) paths.