Under the action of Arctic low temperatures and long-term alternating loads, the fatigue life of the submarine rudder stock mechanism is severely tested. In this paper, the research method of the static strength analysis and fatigue life analysis of the submarine rudder stock mechanism is proposed by combining multibody dynamics, the finite element method, and tests. Based on the three-dimensional model and the motion law of the rudder stock mechanism, a multibody dynamic model is established, and the time history loads of each node of the mechanism are obtained. According to the working temperature range of the submarine rudder stock mechanism in the Arctic, low-temperature tensile tests are carried out. Based on the experimental data, the finite element model is built, and static analysis is carried out. Using the S–N static fatigue design method, fatigue simulation analysis is performed by using nCode DesignLife. The analysis results show that the fatigue life of the submarine rudder stock mechanism decreases significantly when the temperature is reduced from 0 °C to −60 °C. This method can provide a reference for submarine design and life model establishment in the Arctic environment.