Consisting of three forming processes， i.e. edge incurving， flanging and deep drawing， tension driven internal inversion method is a new technology for shaping thin walled metallic round tube into a double layered tubular part with an annular bottom. Based on the study of edge incurving process of tubes， a number of analytical relations are established which reflect the influences of tube size， material properties， mould size， friction condition and scale factor m on the stress and deformation parameters of tubular part in the process before and after partial tube wall in the curling region has wrinkled. Also， some discriminants are proposed for judging if the tube wall in the curling region wrinkles and if the process is practicable for a certain tubular part. Example indicates that when m is in the scope of 0.7 to 0.8， the stress and deformation parameters calculated by formulas match those simulated by metal plastic forming simulation software DYNAFORM， and the conclusions derived from discriminants correspond well with the simulation and experiment results.