A method for simulating the spontaneous, wind-excited vibrations of suspension bridges is described. The approach is based on a numerical model that treats the bridge and flowing air as elements of a single dynamic system; and all of the governing equations are integrated numerically, simultaneously, and interactively. It is shown that the present simulation predicts the same onset of flutter as the analysis of Fung. Unlike Fung’s analysis, the present analysis provides the solution in the time domain, is not restricted to periodic motions or linear equations of motion, and provides post-onset behavior as long as the effective angles of attack are not large enough to produce stall. As a consequence, the present analysis can be a very effective tool for the design of flutter-suppressing control systems. Because the equations are solved numerically, nonlinear supports do not present a problem. In the present work, it is shown how the nonlinear springs lead to limit-cycle responses.