This work will produce new methods for predicting the effects of wind turbulence on motion stability of long-span bridges and to calculate the statistical properties of bridge response when motion is stable. Both, the additive and the multiplicative wind loads are modeled as stochastic processes and the mathematical techniques of random vibration are used in the analysis. A numerical approximation procedure is applied to treat a large combined bridge-fluid system, involving many dimensions in the state space. Improved modeling of aerodynamic indicial functions to include possible oscillatory components for some bridge configurations is considered, using additional experimental results, and the effect of such oscillatory components on stability and response calculations is evaluated. These new methods are useful for the design of new bridges and the modification of existing bridges.