In the structure of single-mast stacker cranes due to external excitation forces undesirable mast-sway may arise. This effect reduces the stability and positioning accuracy of stacker crane and causes increasing cycle time of storage/retrieval operation. Thus it is necessary to reduce the mast sway in some way e.g. via motion control of stacker crane. Controlling of the stacker crane requires an accurate, at the same time quite simple dynamical model. However, the dynamical behavior of stacker cranes depends on the magnitude and position of lifted load. This paper represents a modeling technique based on multi-body modeling approach. With this technique a series of multi-body models are generated with several lifted load positions and magnitudes. In order to keep the final model simple an unstructured uncertainty modeling method is introduced which is capable of covering the effects of varying magnitude and height of lifted load.