For simulating non-Newtonian fluid motion,in this paper a particle-based method is proposed in this paper.Through adding the stress tensor terms into the Navier-Stokes equations and using the essential method of smoothed particle hydrodynamics,a unified model for simulating non-Newtonian fluid is established.The experimental results show that the elasticity and plasticity of the fluid will change with the values of model parameters k and μ.The fluid exhibits more obvious plastic flow and weaker elasticity when k is increased and μ is decreased,conversely,the fluid exhibits stronger elasticity and weaker plasticity when μ is increased and k is decreased.By extending the Navier-Stokes equations,non-Newtonian fluid with various elastic and plastic characteristics can be simulated realistically by using this model.