Platelet aggregation has been modelled as a nonlinear system of viscous flow and pulsating flow based on the Fogelson’s continuum model. By solving nonlinear governing equations and the coupling between flow and platelet aggregates in the cylindrical coordinates using the finite element method, we can see how the platelet aggregation forms under the pulsating flow conditions. Numerical simulations show that the aggregates are stretched by the flow in the dynamic equilibrium of the link forces and background flow. In addition, significant elastic stress can be developed to maintain the shape and integrity of the platelet aggregates.