Elastic impact and contact of spheres are frequently encountered in the field of engineering and science. It is usually treated by the Hertz theory of impact. There are also other theories proposed by Y. Tatara and P. Villaggio. In the present paper, elastic impacts of sphere are analyzed by using the Finite Element Method (F. E. M.). At first, the results from F. E. M. and those from the theories mentioned above are compared. The dependency of the force-compression relation on the impact velocity is examined. Then, the dynamic elastic contact force-displacement relation of sphere is presented. It is thought that this equation can give the accurate force-compression relation for the impacting spheres. It will also give valuable relation for the evaluation of dynamic contact force between particles in the numerical analyses such as DEM.
