As the stress relaxation is the primary cause for the flange connection failure, a type of new muti-cone coupling flange is designed to diminish stress relaxation for the flange connection. Researching on the structure and geometrical property of the new type flange is carried out in order to improve the connection property. Both the theory reasoning and the laboratory testing proved that the flange structure and machined tolerance have effect on the stress relaxation, which is significant for the flange designing, machining and checking.