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The contribution presents an analytical study and finite element simulation of wave propagation into a viscoelastic body. By assumption, waves are provoked by a blast, as the impact load acts on the internal surface of the body (a hollow cylinder). Within the hypothesis of isotropic behavior, the material response is simulated through an incremental modification of the initial (instantaneous) elasticity modulus in accordance with the predefined viscoelasticity relationship. The presented results include simulation of stress and displacement evolutions in specified locations.