This investigation designs a vibration damping treatment consisting of multiple fluidic flexible matrix composite (F2MC) tubes that is bonded to a cantilever beam. The transverse beam vibration couples with the F2MC tube strain to generate fluid flow through an energy dissipating orifice. At resonance, beam vibration induces fluid flow, amplified by the elastic anisotropy of the fiber-reinforced tube wall. Flow through an optimal orifice maximizes energy dissipation, greatly reducing the resonant peaks. The F2MC tubes in this work are three-layer hollow cylinders with a fiber reinforced middle layer that can be modeled with Lekhnitskii's solution. Using Euler-Bernoulli beam theory, an analytical model is developed that enables the design of a multi-F2MC damping treatment for a laboratory-scale aluminum cantilever beam. A compact F2MC-integrated beam prototype has been constructed with two commercially available miniature (2 mm in diameter) F2MC tubes arranged in parallel. Through optimal selection of the attachment locations and orifice size, analysis results show that 32% damping in the first mode is achievable.