Under-water explosion produces the Shock Wave and the Pressure Wave in the water, the former propagates at the same velocity of the under-water sound, and the later does more slowly, and so, there are two types of the response of the Structure subjected to the under-water explosion. The representative research can be seen in the report by R. D. Mindlin and H. H. Bleich¹⁾ on the response subjected to the Shock Wave, and in the reports by P. G. Hodge²⁾, H. Kito³⁾, T. Nagai⁴⁾, K. Hanita⁵⁾, and Y. Hommao⁶⁾ on the response under the Pressure Wave. Their conclusionsare as follow ; Mindlin and Bleich : Elastic uniform radial deformation of the circular cylindrical shell. P. G. Hodge : Plastic uniform radial deformation of the circular cylindrical shell. H. Kith : Magnification of the amplitude of the initial deflection. T. Nagai : Semi-experimental formula presenting the total deformation including the effect of the initial static pressure, shock wave, and the pressure wave. K. Hanita : Semi-experimental formula presenting the buckling distance against the weight of the explosive, but no presentation as to the depth effect. Y.Homma : Generalized buckling condition by the Energy Method. And a simple example is presented. Thus, there is no report treating the buckling of the cylindrical shell subjected to the Shock Wave. Auther presents the buckling distance of the cylindrical shell subjected to the Shock Wave against the weight of explosive and the initial static pressure. Many experimental results are explained by the present theory.