© Institution of Mechanical Engineers. The one-dimensional impact problem in the case of Fung's quasi-linear viscoelastic model is studied for the relaxation function of the standard solid model (or Zener model). Additionally, quasi-linear viscoelastic Maxwell and Kelvin-Voigt models are recovered as limit cases. The results of numerical simulations for some illustrative values of the dimensionless problem parameters are presented. The obtained results can be of interest for biomedical testing.