Passive safety systems in a nuclear reactor allow to simplify the overall plant design, beside improving economics and reliability, which are considered to be among the salient goals of advanced Generation IV reactors. This work focuses on investigating the application of a self-actuated, gravity-driven shutdown system in a small lead-cooled fast reactor and its dynamic response to an initiating event. The reactor thermal-hydraulics and neutronics assessment were performed in advance. According to a first-order approximation approach, the passive insertion of shutdown assembly was assumed to be influenced primarily by three forces: gravitational, buoyancy and fluid drag. A system of kinematic equations were formulated a priori and a MATLAB program was developed to determine the dynamics of the assembly. Identifying the delicate nature of the balance of forces, sensitivity analysis for coolant channel velocities and assembly foot densities yielded an optimal system model that resulted in successful passive shutdown. Transient safety studies, using the multi-point dynamics code BELLA, showed that the gravity-driven system acts remarkably well, even when accounting for a brief delay in self-actuation. Ultimately the reactor is brought to a sub-critical state while respecting technological constraints.