A power system is a nonlinear dynamical system. Understanding the dynamic behavior of a power system is necessary for its reliable operation. An equivalent mechanical model of a power system was proposed by K. Noda to help the physical interpretation of a power system behavior obtained by a mathematical model of a power system. The validity of the mechanical model was confirmed qualitatively. This study gives the quantitative validation of the mechanical model through experiments to assess the accuracy of the analogy between the mechanical and mathematical power system models. To this end, steady-state and transient stability of a power system, which are the local and global stability, are demonstrated. The cause of error of the mechanical model is discussed and the limitation on the application of the mechanical-mathematical model analogy is provided.