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Two tests of composite shells loaded under half-cosine impulsive loadings are discussed. One cylinder which included no other materials was modeled successfully such that calculated results matched test results out to late times. The other cylinder, which included an inner annulus of an elastomeric material, was less successfully modeled, even though the composite material was modeled similarly in both instances. A viscoelastic model and an elastic model were both used to model the elastomeric material, and the viscoelastic model produced significantly better results.