the simulation of the impact response of viscoelasticbodies is developed by computational finite elementmodel. The variational method is developed to drivethe equations of motion. The Lagrange multipliermethod is exploited to impose the nonholmonic contactconstraints and convert the problem form constraintproblem to unconstraint one. The constitutiveequations are expressed in integral form andinvolving relaxation moduli are adopted to describethe nonaging simple material. Generalized StandardLinear Solid (Wiechert) model is adopted to simulatethe internal damping (viscoelastic) behavior of thestructure is exploited in order to drive a recursiverelationship and thereby eliminate storage problem.Newmark constant average acceleration scheme isproposed to integrate the governing equationnumerically and transfer the problem into a staticone for each time increment