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the simulation of the impact response of viscoelastic bodies is developed by computational finite element model. The variational method is developed to drive the equations of motion. The Lagrange multiplier method is exploited to impose the nonholmonic contact constraints and convert the problem form constraint problem to unconstraint one. The constitutive equations are expressed in integral form and involving relaxation moduli are adopted to describe the nonaging simple material. Generalized Standard Linear Solid (Wiechert) model is adopted to simulate the internal damping (viscoelastic) behavior of the structure is exploited in order to drive a recursive relationship and thereby eliminate storage problem. Newmark constant average acceleration scheme is proposed to integrate the governing equation numerically and transfer the problem into a static one for each time increment