RDT (Recursive Diagonal Torus) is a class of interconnection networks for massively parallel computers (MPCs). It consists of recursively structured mesh/torus connections. It has been proved that RDT supports better performances than most direct networks. SINOMP designed for the structure simulation and performance analysis between RDT and those networks is proposed. The simulation results also prove the good performances of RDT. In this paper, the fault-tolerant routing algorithms on the RDT structure are proposed and discussed. They select one of the shortest routes computed with the routing vector on the non-faulty network by using the different rank order. The additional hops are used to send packet only when all the shortest routes have faulty links/nodes. The proposed algorithms need no additional virtual channels for fault tolerant and support a reasonably large number of faults without significantly degrading the system performance.