Vertical vibration analyses of suspension bridges subjected to random wind forces are presented. In this thesis, suspension bridges are modelled as continuous systems. In the free vibration analyses, the exact mode shapes and the natural frequencies are obtained and the results are compared with those obtained by a conventional method assuming the modes as sine functions. Aerodynamic damping effect due to flutter is investigated. Buffeting forces are evaluated considering the cross-correlation of the fluctuating wind components along the bridge span. Numerical example analyses are carried out for two existing bridges, namely Namhae Bridge and Golden Gate Bridge.