Collide of two objects or impact, is one of the main damage initiation reasons. In this paper, impact and damage behavior of elastic and visco-elastic bodies are investigated numerically using the finite element analyses. The results showed that visco-elastic materials, distribute stresses to the edge of model after the impact with a solid body. Furthermore, the impact of elastic and visco-elastic composite materials are analyzed and the variations of stress, displacement, damage energy and the damage patterns during a time period are compared for the two material models. The reduction in the values of stress, displacement and damage energy of visco-elastic material is also determined relative to the elastic composite material.