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We are interested in the dynamic behavior of a system of pipes and vessels filled with liquid, which is a very common configuration in the oil and gas or power generation sectors. Each component of the system is discretized with finite elements under a classical fluid-structure formulation, often referred to as U-P formulation. Namely, the fluid and the structure degrees of freedom (DOF) appear in the coupled system, resulting in an algebraic system of non-symmetric matrices, whose eigenvalues and eigenvectors are sought. The aim of the paper is to propose a new dynamic substructuring method for the efficient solution of the coupled modal problem.