In this work, a corrected symmetric and periodic density reinitialized SPH (CSPDR-SPH) method is proposed and extended to simulate the viscoelastic free surface flows based on the Phan–Thien–Tanner model. The improvements mainly lie in deriving a corrected symmetric kernel gradient, and combining it with a periodic density reinitialization procedure. In addition, a simple artificial viscosity and a simple artificial stress form are adopted. Thus, the CSPDR-SPH method has higher accuracy and better stability than the SPH method, and conserves both linear and angular momentums. The consistency and convergence of the CSPDR-SPH method are justified by approximating a function in one and two dimensions. The merits of CSPDR-SPH method are demonstrated by several benchmarks. The simple flow in a two-dimensional channel is investigated to show the capability of the CSPDR-SPH method to simulate the viscoelastic free surface flow. Then the CSPDR-SPH method is extended to simulate the impacting drop problem. Numerical results show that the CSPDR-SPH method can precisely capture the viscoelastic free surface. The Reynolds number, Weissenberg number and elongation parameter have remarkable effect on the flows. Copyright © 2012 John Wiley & Sons, Ltd.