As the analytical tools of fatigue and brittle cracks, we often use the K value analysis. The solution of K value is formulated by Irwin, Kobayashi, Paris, Ishida and et al. But as for the K value at the complex figure that is often seen in the ship structure, it is not so enough solved. The author is investigating on the analytical solution method of the K value in the complex figure, especially on the selecting boundary stations method and the conformal mapping method. The former method is utilizable for the multi-plane structures composed of thin plates. And the latter method is usefull for the defined problems. This paper dealed with an example of the solution by the latter method. By the method discribed in this paper it is possible to solve the problems of surface cracks in equator rings of spherical LNG tanks, in fillet welded toe and thick pipes, with the circular arc figure of the surface into consideration. The inverse method that is one of the conformal mapping is designated by the change of the coordinate ( X '+ iZ ') = ( X + iZ ) ^-1 And the stress, external pressure, figure and K value of the flat bodies is easily transfered to those of the circular bodies, as shown in this paper. As the results of calculations on some examples, it can be said that the error is about 30% in case of most erroneous value, if we calculate the K value without exact consideration on the figure of free surface, such that the arc to be a flat.