A general multidegree-of-freedom vibration system with mass-spring dynamic absorbers is theoretically analyzed. A general expression of the steady-state response is derived by making use of the eigenfunction expansion and receptance method. A method for the optimal tuning of the natural frequency and damping of an absorber is established. As an example, a numerical calculation for a cantilever is carried out, The results confirm the theoretical analysis and show the effectiveness of the absorber for vibration reduction. An improved method of optimal tuning for a system which has multiple absorbers for suppressing multiple modes of vibration is also derived.