Practical applications of Lyapunov's direct method to transient stability analyses of multimachine power systems have been obstructed by the well-known conservative nature and the computational difficulty accompanying the usual critical value of Lyapunov function. These problems have been solved in this paper by introducing a new critical value for the first swing stability, and by developing a efficient method of calculating it as well as one of taking account of transfer conductances. These methods have been applied to a transient stability analysis of a 10-machine power system, and yielded results of practical significance.