Over the last 10 years, significant changes have taken place in the world of container shipping. The size and the speed of the quay-side crane have been increased considerably. As a result, the stiffness of a crane is decreased and the sway oscillation of cargo may become violent. The purpose of this paper is to determine the design force caused by the sway oscillation of the cargo, lifted by four ropes, with an initial fleet angle, and the governing equations of the lifting system for an anti-sway control system design.