Abstract: In a complex cantilever structure there are some closed resonance peaks in the vicinity of 20Hz, causing a serious bending moment at its root. The application of multiple dynamic absorbers to reducing its vibration level is proposed in this paper. Six absorbers are hung on a given section of the structure to overcome the drawback of the usual tuned absorbers, i. e. excessive sensitivity to the tuning parameters. They can vibrate in all directions following the structure, but their stiffness and damping parameters of these absorbers are different from each other, so that their frequency range is made wide enough to cover the resonance frequencies.In search of the conditions for minimizing the bending stress of the structure and for the sake of studying the effects of the parameters on the dynamic response, a great number of response curves at the top of the structure, bearing the harmonic excitation from the base movement, are calculated as the parameters of these absorbers vary in a considerable range. Since the damping of the structure is very small and that of absorbers are large enough, so it is a dynamic analysis problem with non-proportional damping. This problem has been solved by a complex eigen-solution method and a modal synthesis method in the present paper.