With the development of drilling technology in complex structural wells, it is difficult to run casing by conventional methods due to the complex change of deviation angle and azimuth angle with well depth. The running-casing with rotating technology can solve the problem of running casing effectively, but few theoretical analysis was reported in this field, which increases the blindness and inefficiency of the application of running casing with rotating technology. The mathematical model of rotating casing running was obtained by using the advantages of soft rod and rigid rod model comprehensively and considering the influence of wellbore trajectory on model calculation conditions. The correctness of the model was verified by comparing the load of the hook with the simulated axial stress. On this basis, the friction of casing under normal and different rotating speeds was discussed, and the friction distribution characteristics under different friction coefficients were analyzed. The case analysis indicates that the casing friction with rotation is less than that of conventional method in the same well depth, and the faster the rotation speed is, the smaller the casing friction is. When the rotation speeds of casing are 15 r/ min and 20 r/ min, the decrease degree of the friction resistance at the bottom are 12. 13% and 19. 17%, respectively. The greater the slope is, the higher the friction is, leading to the casing be more difficult to run into the specified depth. The greater the friction coefficient of drilling fluid is, the higher the difficulty of running casing is. The friction coefficient of open hole section is 0. 21 and 0. 29 at the depth of 1 401. 5 m, corresponding to the friction of conventional casing be 46. 51 kN and 57. 49 kN, respectively. The developed model can accurately predict casing friction, which has guiding significance for running casing in complex structural wells. [ABSTRACT FROM AUTHOR]