In the previous paper by authors, the time histories of wave conditions, with which 38 ship encountered during sailing in the North Pacific over a period of 14 years, were analyzed, and were proved to show a certain pattern in stormy sea states. In this paper, loading model -Storm model- is proposed for random loading fatigue tests of ship structurs, and fatigue tests under “Storm model” were performed for specimens with boxing fillet welded attachments which were one of the most important ship structural components from a view point of fatigue strength. Palmgren-Miner's rule was examined by analyzing the fatigue test results. The main points made in this paper are as follows ; 1) The effects of mean stresses and residual stresses were recognized under “Storm model” conditions as well as constant amplitude loading. 2) The fatigue limits under “Storm model” conditions are liable to become higher than that of a constant amplitude test which is stress amplitude according to fatigue life of 2 millions cycles. 3) Scatters of fatigue lives estimated by means of Palmgren-Miner's rule for “Storm model” conditions are as same as in constant amplitude fatigue tests.