Recent experimental works in our country on the bodily collapse of ring-stiffened circular cylindrical shells subjected to hydrostatic external pressure are almost concerned with welded and so initially deformed models in order to apply the results directly to the design of submarine hulls. But the results can not satisfactorily be explained by the analyses which makes use of exsisting theories, hereby the method of analysis which accommodates to such imperfect models seems to be needed very much. This report deals with a method for estimating the collapse pressure which relates to material strength and initial out-of-roundness as parameters. This method is based on the consideration that, when ring-stiffeners have some initial out-of-roundnesses and the model is loaded by uniform pressure, the stiffeners contract gradually while being bent in a certain circumferential mode, and finally when at least three plastic hinges occur at the adjacent positions on them, the stiffeners collapse locally and immediately after that a total model collapses generally. Some experimental results are refered to ascertain this method.