Abstract: Aimed at the forced coupled longitudinal-transverse vibration of flexible hoisting systems, the governing equations and energy equations of the coupled vibration of the flexible component with arbitrarily varying length are developed using the Hamilton’s principle. The Galerkin’s method is used to discretize the governing equations，which can be solved with numerical methods. The elevator hoisting system is analyzed to evaluate the proposed theoretical model. The results of simulation show that under typical conditions, the elevator system motions with coupled vibration, in which transverse vibration is dominant; while a nonstationary vibration may occur in the upward trip of elevator car. These phenomena have already been observed in practice.