Bend stiffeners are polymeric structures employed to ensure a smooth and safe transition in the upper connection of risers and umbilical cables, protecting them against accumulation of fatigue damage and excessive curvatures. Recent failures have stimulated a better understanding of the mechanical response in order to increase the reliability in design and analysis of bend stiffeners. This work presents a mathematical formulation that represents the system riser/bend stiffener considering geometric non linearity and polyurethane with viscoelastic behaviour, an inherent characteristic to polymers. The following assumptions are considered: cross-sections remain plane after deformation, large deflections are accepted but it is a small strain bending problem, the self-weight and external forces are disregarded and the material is assumed with linear viscoelastic behaviour. The curves that represent the viscoelastic response of the material have been raised by means of creep tests, whose specimens were cut from actual bend stiffeners. The time dependent data obtained in the experimental tests were well approximated by a third order Prony series which describes the creep function. The set of four first order non linear ordinary differential equations results from geometrical compatibility, equilibrium of forces and moments and linear viscoelastic constitutive relations. The numerical solution of the problem is obtained using a one-parameter shooting method. The results are then compared with the consolidated numerical solution for linear elastic material. It is concluded that the viscoelastic phenomena can lead to excessive curvatures on the upper terminations of risers and umbilical cables if the polymeric structure were designed considering elastic behaviour. The correct characterization of the viscoelastic properties of polyurethane used on bend stiffeners must be taken into account when accurate analysis is desired.