This paper introduces a novel mathematical model that using the Hamiltons' principle to set up coupled dynamics model of gantry cranes with flexible cable. By using finite element method to solve the equations that govern the motion of the crane system. Numerical simulations for the coupled dynamics model are presented for various operating conditions, and compared to the simulation results of the model with cranes made with rigid cable under the same working conditions. From the consequence, we can get the effects of cable's flexibility on gantry crane's kinematical properties; According to the conclusions, this paper defines two parameters of the gantry cranes, and qualitatively analyzes the two parameters' effects on dynamics kinematical properties of gantry cranes.