Shakedown and ratcheting behaviors of thick-walled cylindrical vessels with radial openings subjected to cyclic thermomechanical loadings are investigated by the inelastic finite element analysis. Different shakedown and ratcheting responses are described in the modified Bree diagram considering the influences of various opening radius ratios , thickness ratios as well as different axial stress states. Then, two simplified shakedown assessment methods of perforated cylinders are discussed. The results indicate that elastic/plasticity shakedown boundary reduces significantly owing to the presence of a radial opening while varies slightly with the opening radius, which can be defined as 1.2 approximately in the modified Bree diagram for conservative elastic/plasticity shakedown evaluation. Moreover, shakedown/ratcheting boundary decreases significantly with increasing the opening radius or decreasing the axial stress. Finally, comparing with the calculated results, the two simplified methods are verified to be accurate and intuitive to estimate the shakedown behaviors of perforated cylinders under various thickness and opening radius conditions.