AbstractThe well-known Volterra integral equation in linear viscoelasticity is treated to characterize the response of nonlinear viscoelastic materials. In this context, a procedure is presented which includes a differential approximation of the time-dependent kernel and an optimization procedure and leads to an optimum selection of certain parameters such that the deviation of the theoretical results form the experimental data is minimal. The formulations are then applied numerically to the case of natural cellulose fibres by using available experimental data on the relaxation of such fibres. The results of the investigation prove the close accuracy of the predictive ability of the model within the range of strain levels considered.