A large number of cracks of web stiffeners on deep bottom transverses at their cut-outs which were provided to let longitudinals pass through them. It is required to estimate load condition of stiffeners at the cut-outs and fatigue strength of them. In this paper authors describe about result of study on load condition of stiffeners and frequency of damaged stiffener, and some opinions about mechanism of initiation of the damage. Authors study on the long-term distribution of wave induced lateral pressure on bottom shell including inside pressure caused by ship motions and estimate the distribution of wave induced stress of the stiffeners. From our study it is clarified that the distribution is described approximately by Weibull distribution (exponential distribution). Supposing that the distribution of cycle of load to failure is described by logarithmic normal distribution, amplitude of still water stress is constant and distribution of wave stress is Weibull distribution, authors develop a new method of analyzing the relation between design stress and frequency of damaged stiffener. The method is very useful because it is also applied to analysis of fatigue damage of longitudinal member etc. By our study the load condition in wing tank is evaluated to be worse, so it is expected that the frequency of wing tanks is higher than that of center tanks. From the result of inspection of actual ships, the same result is found. Character of the frequency, difference of the frequency by species of tank and by ships' age etc., estimated by our analysis is compared with the result of inspection in the same manner. It is concluded that damage affected by vibration of transverses may be found in the after tank part. A new allowable value of design stress is guided by our method which is a little higher for stiffeners without back-brackets than the value which was suggested by the 120th Research Committee of Shipbuilding Research Association of Japan.