To investigate the effects of stepped buoyancy and sectional inertial forces induced by buoyancy modules on the vibration characteristics of marine fluid delivery risers, a vibration model of the riser under combined internal and external flow was established based on the Euler-Bernoulli beam theory, in which the non-uniform axial tension and piecewise inertial effects induced by the buoyancy modules were considered. The governing equations were solved using the Generalized Integral Transform Technique, and the validity of the model was verified through comparison with the Homotopy Perturbation Method. On this basis, the effects of buoyancy-to-weight ratio and relative installation position of the buoyancy modules on the critical flow velocity, natural frequency, and vibration amplitude of the riser under different operating conditions were analyzed. The results show that appropriate selection of buoyancy ratio and installation position can increase the critical flow velocity and reduce the vibration amplitude, thereby enhancing the vibration resistance of the riser. This study provides a theoretical basis for the parameter design of buoyancy modules and structural optimization of risers, and is of significance for improving the dynamic analysis methods of risers as well as the overall safety of offshore oil and gas operations.