To meet the economic, social and infrastructure needs of the community for safe and efficient transportation systems, long span bridges have been built throughout the world. Long span bridges are one of the most challenging kinds of structures in civil engineering. The cable-stayed bridges are of great interest mainly as an alternative and a more economic solution than the one of suspension bridges. In addition, the fiber reinforced polymer (FRP) composites are, nowadays, successfully used for constructing modern bridges, where the significant weight saving provides additional benefits. Because of the great flexibility, modern long-span cable-stayed bridges are usually very susceptible to dynamic loads especially to the earthquake and strong winds. Therefore, the earthquake-resistant and wind-resistant designs become one of key issues for successful construction of bridges. The objective of the present research is to develop a very efficient spline finite strip technique, for modelling and analysis of both conventional and hybrid FRP cable-stayed bridges. The study falls into the categories of bending, free vibration, seismic, and aerodynamic flutter analysis. The spline finite strip method (SFSM) is one of the most efficient numerical methods for structural analysis of bridges, reducing the time required for estimating the structural response without affecting the degree of accuracy. In the finite strip method, the degrees of freedom could be significantly reduced due to the semi-analytical nature of this method. However, the previous versions of SFSM are not able to model the entire bridge system. For that reason, the structural interactions between different structural components of the bridge could not be handled. In addition, the vibrations and displacements of the towers and cables could not be investigated. In the present formulation, all these obstacles have been eliminated. Moreover, the proposed finite strip technique is very efficient and accurate due to the drastic reduction in the formulation time, simplicity of data preparation, rapid rate convergence of the results, and the semi-analytical nature. Last but not least, and for the first time, a fully finite strip solution is extended to the area of wind engineering. Using the spline finite strip discretization, the aerodynamic stiffness and mass properties of the long-span cable-stayed bridge are derived. The aerodynamic properties along with the structural properties of long-span plates and bridges are formulated in the aerodynamic equation of motion and are used to analyze the flutter problem. The accuracy and efficiency of the proposed advanced finite strip method is verified against the finite element and field measurement results. The results demonstrate that this methodology and the associated computer code can accurately predict the dynamic and aerodynamic responses of the conventional and FRP long-span cable-stayed bridge systems. The outcome of the present research will lead to a comprehensive structural analysis of bridges in the framework of the proposed discretization which is more efficient and straightforward than the finite element analysis.