As far as ship's cargo handling devicesareconcerned, the derrick system has been used comprehensively in the marine. Even though there are several new devices for ship's cargo gear, such as gantry crane, jib crane adn self unloader, the derrick system, with its improved rigging method, still retains its utmost reputations among ship's owners. Therefore the method of calculating the system's militating stresses in the course of cargo operation needs to be more convenient and analytical. Here the author attempts to introduce the calculating method of stresses by means of vector analysis. The calculating method is able to analyze the stresses acting in every part of the cargo gear systems, such as union purchase, slewing or its modified system.