The present dissertation deals with the risk assessment of bridge decks prone to vortex induced vibrations (VIV), which is presently recognized as a key issue in the design of flexible bridges. A procedure is proposed to quantify the risk associated with VIV of bridge decks. The framework adopted is in line with the general risk management framework developed by the IGC 802. Performance-based-design approach is followed and the risk is quantified by using a modified version of the PEER equation. First, the hazard analysis is developed. It consists in evaluating the probability of the hazard (wind speed and direction) by means of Weibull distribution. The wind data are also analyzed by using a hybrid model, which consists of estimating the model parameters without considering wind calms. The results are compared with those obtained through the classical approach. In the second part of the dissertation the structural vulnerability analysis is conducted. It evaluates the probability of the structural response during VIV. A careful revision of the state of the art is firstly reported on both the phenomenological aspects and mathematical modeling of VIV of bluff bodies. It led to the conclusion that no model is able to provide reliable predictions of the structural response at values of the Scruton number different from that at which the aeroelastic parameters are estimated. In this work, the Ehsan-Scanlan model (E-S model) was studied in depth because it is considered suitable for practical applications to bridge decks. Wind tunnel tests were performed to apply E-S model to a idealized case study. Highlighted in this analysis is the physical coherence of the van der Pol-type equation used to model VIV of structures prone to wind excitation. Even though the validity of the identification procedure employed in E-S model to determine the aeroelastic parameters of the model is demonstrated, a limit of the procedure is observed when the limit-cycle oscillation amplitude is estimated from experimental signals. In addition, an alternative identification procedure is proposed based on the direct numerical solution of the nonlinear differential equation. In the third part of the dissertation the application of the developed procedure to a case study is reported. The effects in terms of risk due to the different assumptions standing behind the procedure are highlighted. Finally, the perspectives of future developments of this research work are discussed.