The current tendency toward light weight and fast machines has lead to a need to suppress vibration of flexible dynamic systems. Input shaping is an efficient tool to eliminate transient and residual vibration caused by motion of these systems. This paper proposes a new formulation of the design method for multi-mode input shapers to eliminate residual vibration in flexible dynamic systems. The essence of the proposed method is to minimize the number of impulses to be n+1 for n-mode input shapers. This paper also suggests a solution procedure to solve the complex-valued nonlinear matrix equation for the input shapers. The proposed method is applied to two-mode input shapers. This paper discusses characteristics of several input shapers obtained under the same condition. Simulations and experiments show that the proposed method is very useful for designing multi-mode input shapers.