On highway and railway lines, skew bridges are employed when the alignment intersects obstacles at non-orthogonal angles. The skew angle generates torsional moments in the bridge even when the applied loads are vertical and centrally positioned. In this study, an analytical method based on a simplified Euler–Bernoulli beam element model is used to perform the dynamic analysis of high-speed railway bridges, with particular attention to bridges with hollow-slab cross-sections subjected to high-speed Talgo 250 train loads. The influence of the skew angle is taken into account to determine the coupled flexo-torsional modes and subsequently dynamic vibrations. The analytical results are compared with those obtained from a three-dimensional finite element model (3D-FEM). Using the analytical approach, parametric studies are carried out to examine the effects of factors such as the skew angle, structural stiffness through the elastic modulus, and variations in cross-sectional shapes.