While the moving load problem has received a lot of attention in the context of bridges traversed by road or rail vehicles, the same cannot be said about ship unloaders where research is limited and typically focused on displacements. In ship unloaders, the moving system is composed of a trolley, attached grab, and payload. The interaction between the moving system and the lifting boom on which the trolley travels can lead to high stresses. Given that the stress ranges and associated number of cycles experienced by a section of the lifting boom determine its fatigue life, these stresses must be assessed as accurately as possible. For this purpose, dynamic transient analysis of the effects of a payload-carrying trolley moving along the boom is carried out using an equivalent planar finite element model. Results show how bending stresses are affected by the inertial forces of the structure and the moving load, the ratio of the mass of the load to the mass of the boom, the flexibility of the moving system, and the payload mass and its swing angle.