The usual method to derive the intermittent motion of a system has some limitations, such as the need to specify the value of the coefficient of restitution. In deriving the value of the coefficient of restitution, Newton, Poisson or Stronge method is used. All of the methods have problems to cause energy contradiction and give the different value in non co-linear collision or collision with friction. This is due to the assumption of rigid body. For the analysis of the flexible body dynamics under impact, authors proposed wave propagation theory. Wave propagation theory is the method which is considered to be superior to the Newton method for its rigorous sense. By using wave propagation theory, we discuss the characteristics of the coefficient of restitution in detail and confirm that the values of the coefficient of restitution greatly depends on the conditions of impact.