The vibrations of pipes and their supporting beams caused by the tank bulging mode are analyzed. A computationally efficient semianalytical approach is presented by introducing a local velocity potential for each pipe and developing a reduced order model for the frame structure consisting of the pipes and their supporting beams. To enable the analysis, the system of governing equations and boundary conditions is derived in a variational form. Numerical results show that large bending stress occurs in the supporting beams attached to the lower part of the tank wall. This bending stress can be reduced by decreasing the outer diameter of the supporting beams based on the fact that the dependence of the bulging-mode-induced displacements of the supporting beams on their stiffness is weak. This stress reduction method does not increase but decreases the stiffness of the supporting beams and therefore the cost, unlike many methods for improving structural reliability. A method for reducing the axial compressive stress in the supporting beams is also investigated.