Regarding the external sling load system of heavy-lift helicopters, the influence of the law of lifting point position on flight control stability characteristics has not been distinctly explained. To address this challenge, this paper constructs a sling load flight simulation model based on multi-body dynamics. Overall, the proposed model consists of four parts, including the rotor aeroelastic coupling model, the fuselage rigid body dynamics model, the flexible sling model, and the slung object rigid body model. Furthermore, through the hub six-degree-of-freedom rigid model and the flexible sling model, this paper realizes the dynamic coupling between the components. On this basis, taking the CH-53E heavy-lift helicopter as the research object, this paper utilizes real flight test data to validate the multi-body dynamic model. Subsequently, this paper systematically analyzes the influence of different lifting points’ lateral position, sling load mode, load-mass ratio, and forward flying speed on helicopter control stability characteristics. Simulation results indicate that the lifting point location exerts a significant impact on the helicopter’s trim attitude angles and dynamic stability. Of them, the lifting point location of the front center of gravity is the optimal in terms of trim characteristics and eigenvalue distribution. Furthermore, within a certain flight speed range, the lifting point of the front center of gravity demonstrates superior speed adaptability and system robustness. Apart from providing a solid theoretical basis for the lifting point layout design of the external sling load system of heavy-lift helicopters, the research results have important engineering application value for improving the safety of sling load flight of heavy-lift helicopters.