In this paper, a trolley-axis-based swing angle description is proposed for a 2-dimensional overhead crane, and then a new nonlinear dynamic model for the crane is derived based on the proposed swing angle description. The dynamic model is equivalent to that for 3-link flexible robots having only the first flexible mode. Furthermore, when the model is linearized around the vertical stable equilibrium, it becomes decoupled and symmetric with respect to the travel and traverse axes of the crane. From this result, a decoupled feedback control method is proposed based on the linearized model via the loop shaping and the root locus methods. Theoretical and experimental results show that the proposed control method guarantees not only fast damping of load swing but also accurate control of trolley position with sufficient damping for the 2-dimensional motion of the crane.