"Highway bridges are crucial parts of the civil infrastructure which require special attention at the time of their analysis and design. Box girder deck systems are amongst the most popular types of highway bridge structures and the understanding of their behaviour under different loads plays an important role in their structural design. Therefore, an accurate assessment of the response of these bridges under these loads is of great importance. Box girder bridges are essentially thin-walled beams having closed or a combination of closed and open cross-sections. The behaviour of these thin-walled structures under an arbitrary loading scenario is quite complex, primarily due to the cross-sectional warping (out-of-plane warping) and the distortion of the sections (in-plane warping). The accurate calculation of warping displacements has been the area of many research studies because the variation of warping displacements over a cross-section does not follow a standard pattern. With the help of a detailed Finite Element Analysis (FEA), it is possible to obtain results which may be reasonably close to the exact three dimensional (3D) elasticity solutions of these thin-walled structures. However, this approach involves significant computational resources and efforts, especially for bridges having complex geometries. The use of this modelling approach is not feasible, particularly at the preliminary design stage when the analysis is typically performed many times and the design is being modified and improved iteratively. On the other hand, a specific feature of typical box girders is that one of its dimensions (length) is very large compared to the other two dimensions. Utilising this trait, many researchers have tried to condense the 3D problem into a one-dimensional (1D) problem and treat these structures as beams. Although this approach makes the analysis highly efficient, the existing beam theories involve many approximations in order to account for out-of-plane warping and distortion of these structures. This can affect the accuracy of the solution significantly for thin-walled box girder bridges. In the present thesis, a novel method is introduced which can offer a very accurate solution to the problem and at the same time the method is computationally efficent. The proposed technique splits the 3D elasticity problem into a two-dimensional (2D) cross-sectional problem and a 1D beam problem. The 2D beam cross-sectional problem is solved using a 2D finite element discretization where the effects of in-plane warping as well as out-of-plane warping are considered. The 2D finite element analysis generates the 'exact' constitutive matrix (or stiffness matrix) for the beam cross-section which ensures proper coupling between the different modes of deformation. This cross-sectional stiffness matrix is then used in the 1D beam analysis based on a usual 1D beam finite element model. The stress resultants obtained from the 1D beam analysis and the results obtained from the 2D cross-sectional analysis are used to determine the warping displacements and finally recover the 3D stress and displacement fields of the thin-walled beams. The computational efficiency of this approach is significant in terms of prediction of the 3D response of these structures. In order to implement the method, computer programs were developed in FORTRAN specifically for the present purpose. The major research contributions of the current study are presented in the form of three journal papers and one conference paper. Firstly, the mathematical formulation of the method is presented in details and its accuracy is examined by the analysis thin-walled girders having different cross-section configurations under various loading conditions. The results are then validated against those obtained by 3D FE models of these structures. In the second paper, the method is extended to dynamic analysis of box girder superstructures. Numerical examples of thin-walled box girders are solved by the proposed approach under dynamic loading (e.g. time varying and moving loads) to show its performance. The free vibration analyses of these structures are also carried out and the results are compared with the results obtained by 3D finite element analyses of these structures. Finally, the behaviour of straight and curved thin-walled box girders is investigated through experimental studies. Detailed 3D finite-element analysis of these girders is carried out and the results are compared with the experimental results. Also, the experimental results obtained for the straight specimen are used to validate the proposed analysis approach. Additionally, the vibration frequencies of the specimens are measured using the data obtained from their impact excitations. The results obtained from the proposed method are found to have a very good correlation with the 3D FEM in all investigations. Considering the level of accuracy and efficiency required for the analysis of bridge super-structures, the proposed modelling approach seems to have a very good potential in its application for different problems. It is expected that this research will initiate further developments of this technique for its extension in the analysis of wide variety of bridge configurations (e.g. curved, composite) and for solving various problems (e.g. geometrical nonlinearity)." -- abstract, leaves i-ii.