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Flexible Matrix Composite (F2MC) tubes are emerging technologies, which can provide lightweight, compact vibration control when attached to a vibrating structure. This work presents a new model for solving a problem of vibrations in cantilever beams with attaching F2MC tubes as patches that provide passive vibration control. Mathematical model of the compound system of patches of F2MC tubes integrated on the beam was derived. The governing equations depend on Euler-Bernoulli beam theory and Lekhnitskii’s theory of elasticity. This study examined new model’s performance for damping with variation in tube size; bonding position of the patches on the beam in two different cases: on the beam through changing the distance between two them; one patch above and the other under the beam. Analytical results demonstrate that the proper tuning the size of tubes as a function of inner layer radius; and integration points are basic parameters for passive vibration control. They achieve reductions in response amplitude at the first vertical bending mode effectively.