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This research focuses on studying and investigating a ship’s propulsion system. A single shaft propulsion system which consists of gas turbine, gearbox, and a propeller will be considered as a model for the ship’s prolusion system. The system will employ a method of distributed lumped parameter modeling where an arrangement of the following configuration will be analyzed. This configuration comprises of rotors (representing gas turbine, gearbox, and propeller), bearings, and a shaft connecting the three rotors. A block diagram representing the system will be formulated and the shear stresses along the shaft and the angular speeds of the rotors will be computed. The system will be distributed to check its response and stability. The system once built up will be simulated to be tested under different conditions. Since there are many factors that can affect the system, it will be simulated based in certain assumptions and few conditions will be selected. The transient response of the system will be computed against predetermined inputs and scenarios. The results will be presented by graphics and the results will be commented upon.Same procedures will be applied on one more condition to test the propulsion system against sea mine that in result to the mine exploding underneath the propeller it will take off the propeller where the third rotor will be eliminated during the simulation.