Abstract: The smoothed particle hydrodynamics (SPH) method isapplied to simulate the viscoelastic flows governed by the PHan-Thien-Tanner(PTT) constitutive equation. First of all, the validity of the SPH methodfor viscoelastic flows is verified by comparing the numerical solution of aPTT fluid in the planar Poiseuille flow with those in literatures. And then,a viscoelastic free surface flow is simulated to consider about a drop of aPTT fluid impacting a rigid plate. Furthermore, the effect of theelongational parameter is investigated. The results show the flexibility ofthe SPH method for viscoelastic free surface problems. In particular, asimplified artificial stress is adopted to resolve the problem of thetensile instability. Numerical results obtained are in good agreement withthose simulated by other mesh-based methods.