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Elastic coupling can isolate the vibration transmission between the main engine and propulsion shafting. Considering the compact equipment arrangement and limited installation space in underwater vehicle tail， a new rubber coupling is designed and investigated. The calculation model of this coupling is built by using the finite element software Abaqus， and the ultraflexible property of rubber material is represented by the Mooney-Rivlin model. The influence of the number of wedges and the structure of hole on the strength and static parameter of the coupling is analyzed. Comprehensive performance comparison is given between the new rubber coupling and the high quality product with the same torque. The result shows that the coupling meets the structural strength requirements and the performance is superior to the contrast product， meanwhile it has smaller installation space requirement. The result provides a reference basis for realize its engineering application.