Abrasive flow machining (AFM) is a nontraditional surface finishing method that finishes complex surface by pushing the abrasive media flow through the workpiece surface. The entrance effect that the material removal increases at the entrance of changing the cross-sectional flow channel is a difficult problem for AFM. In this paper, the effects of media rheological properties on the entrance effect are discussed. To explore the effects of the media’s viscoelasticity on the entrance effect, two sets of media with different viscoelasticity properties are adopted to study their rheological and machining performances in the designed flow channel with a contraction area. The rheological properties are tested by frequency sweep and characterized by the Maxwell viscoelastic model and the Carreau viscous model. In the experiment, the variation of the profile height (ΔH) and the variation ratio of the roughness (ΔRa) on the workpiece surface are measured. Moreover, numerical simulation results under different constitutive equations are compared with the experimental results. It shows that the numerical simulation results of a viscoelastic model have a better agreement with the experimental results than the viscous model, and the increase of the viscoelasticity makes the entrance effect be exacerbated, which can be predicted by the viscoelastic numerical simulation.