Polymer properties, i.e. viscoelastic characteristics, may pose a non-negligible impact on the axisymmetric analysis, especially on the axial structural damping behavior. An available mechanical model taking viscoelastic into account is established for capturing such parameters as axial strains and forces on each layer, axial stiffness and so on. In this paper, the flexible riser is divided into helical and cylindrical elements to carry out the mechanical analysis due to the complexity of structure and material property. Prony Series is used to describe the creep and relaxation behavior of material viscoelasticity. A viscoelastic solution is obtained using the correspondence principle. Finally, a case study is performed and some interesting results are presented.

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