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Numerical simulation of blood flow through a capillary using a non-linear viscoelastic model. In this article, a periodic developing blood flow in a capillary is simulated using a non-linear viscoelastic model for the first time. Here, the Giesekus model is used as the constitutive equation, and based on the experimental data, the best value for the mobility factor and zero shear rate viscosity are derived. The numerical solution of the problem is obtained using the finite volume method. The algorithm of the solution is pressure implicit with splitting of operators (PISO). The simulation carried out using the Giesekus, Oldroyd-B and Newtonian models and the results indicate that the Giesekus model presents a more accurate solution for the stress and velocity fields than the Newtonian and Oldroyd-B models. The previous studies on this problem were restricted to the linear and quasi-linear viscoelastic models. It is shown that only non-linear viscoelastic models can accurately describe the experimental data of unsteady blood flow in capillaries.