We performed a numerical study for the cessation of Couette flow of non-Newtonian fluids with a yield stress. We solved this problem by employing our recently developed constitutive model for such fluids [H. Zhu, Y.D. Kim, D. De Kee, Non-Newtonian fluids with a yield stress, J. Non-Newton. Fluid Mech. 129 (2005) 177]. In the numerical simulation we adopted the finite volume method with an implicit scheme in time. We computed the finite stopping times for fluids with different yield stresses and shear thinning properties. Our numerical results show that the yield stress play a important role in determining the finite stopping times for non-Newtonian fluids with a yield stress; on the other hand, the shear thinning property does affect the finite stopping times in that the larger the degree of shear thinning, the longer the finite stopping time. The present study is an extension of the previous work by Chatzimina et a]. [M. Chatzimina, G.C. Georgiou, I. Argyropaidas, E. Mitsoulis, R.R. Huilgol, Cessation of Couette and Poiseuille flows of a Bingham plastic and finite stopping times, J. Non-Newton. Fluid Mech. 129 (2005) 117], in which only Bingham fluids are considered. (C) 2007 Elsevier B.V. All rights reserved.