An analytical solution for the coefficient of restitution of a mass colliding with a slender rod or beam was presented. The colliding body was regarded as the attachment of the target, so the problem was transformed into a normal vibration problem using DMSM (Direct Mode Superposition Method). The separation moment was obtained by setting the impact force as zero. It can be concluded that,when only elastic impact is considered, the coefficient of restitution is determined by not only the material property of the target, but also the mass ratio of the colliding body to the target, and the boundary condition of the target. However, the initial velocity has no effect on the coefficient of restitution.