The structural-aerodynamic modelling and dynamic stabilization of a three-dimensional suspension bridge model is considered. Our emphasis is on investigating the effectiveness of leading and trailing edge flaps in suppressing aeroelastic instabilities. The East Great Belt Bridge is chosen as a design example, and its aeroelastic limits are computed using both thin aerofoil theory and flutter derivatives. The problem is cast in an efficient reduced size finite element formulation with aerodynamic forces expressed in the Laplace domain by use of a high-fidelity rational function approximation. Circulatory aerodynamic forces are modelled using a feedback loop for every element, and the problem is expressed in a form suitable for implementation of modern control techniques. The structure's full multimodal response is considered, and numerical predictions show very good agreement against experimental data from the literature. In order to account for modelling errors and uncertainties while designing the controller, elements from robust control theory are invoked. The stability and robustness of the bridge when fitted with flaps controlled by optimal and suboptimal H controllers are discussed for varying lengths of control surfaces along the suspended span as the optimum configuration for aerodynamic performance is investigated. Copyright (c) 2016 John Wiley & Sons, Ltd.