A novel approach based on the Lyapunov decomposition-aggregation method is developed to analyze shaft stability in power systems. The power system including the turbine-generator shaft, flux decay and voltage regulator is decomposed to two isolated subsystems: mechanical subsystem and electrical subsystem. The mechanical subsystem is converted to a standard Lure control system that is analyzed by an improved Lure Lyapunov function. The stability of the power system at the equilibrium points is discussed in detail. The stable operation region of the system is obtained. Case study demonstrates the effectiveness of the proposed method. This study has shown the potential benefits and validity of Lyapunov direct method in the shaft torsional oscillation analysis.