This paper presents a novel approach for damping the vibration of a cantilever beam by bonding a fluidic flexible matrix composite (F<sup>2</sup>MC) tube to the beam and using the strain induced fluid pumping. The transverse beam vibration couples with the F<sup>2</sup>MC tube strain to generate flow into an external accumulator through an orifice that dissipates energy. The energy dissipation is especially significant at the resonances of the cantilever beam, where the beam vibrates with greatest amplitude and induces the most fluid flow from the F<sup>2</sup>MC tube. As a result, the resonant peaks can be greatly reduced due to the damping introduced by the flow through the orifice. An analytical model is developed based on Euler-Bernoulli beam theory and Lekhnitskii’s solution for anisotropic layered tubes. In order to maximize the vibration reduction, a parametric study of the F<sup>2</sup>MC tube is performed. The analysis results show that the resonant peaks can be provided with a damping ratio of up to 13.2% by tailoring the fiber angle of the F<sup>2</sup>MC tube, the bonding locations of the tube, and the orifice flow coefficient.