Ratcheting assessment under multiple combined thermo-mechanical load cases has always been an intractable problem in pressure vessel design by analysis. Ratcheting is not allowed in the current widely adopted ratcheting assessment method based on ratcheting boundary, which is conservative and only applicable to single cyclic load case. Whereas, the ratcheting analysis based on elastic-plastic finite element analysis cycle by cycle is computationally heavy and costly. In this paper, a simple and practical ratcheting assessment method based on cumulative damage is proposed. The method is abbreviated RACD method, which is an evaluation method of plastic ratcheting strain for prevention of ratcheting collapse and allows the structure to enter the ratcheting state. Moreover, it has low computational cost and can be applied to the ratcheting assessment of combined load cases. The validity of the RACD method has been verified by the Bree model and application example in this paper. It can be indicated that the linear damage accumulation theory is applicable to the cases where multiple load cases are applied independently and sequentially, but it is not suitable for the combination of multiple loads applied alternately. The load unit assessment method proposed in this paper can effectively deal with the ratcheting assessment problem for alternating combined load cases.