Abstract: The abrasive polishing of 304 stainless-steel surfaces with quasicrystal powder were mathematically formulated with single-particle model and numerically simulated in finite element method.The influence of the quasicrystal abrasive shapes,including spherical-ball and triangular/trapezoidal/stripe-shaped flakes,on the reinforcement and wear-rate of stainless steel surfaces was investigated.The simulated results show that depending on the grain-shape,the quasicrystal abrasive outperforms the conventional diamond and alumina abrasives.The impact of quasicrystal grain-shape on the equivalent stress can be listed in a descending order:spherical-ball>stripe-shaped flakes>triangular flakes.The longitudinal effect of the quasicrystal on the equivalent stress and its depth is stronger than that of either diamond or alumina.When it comes to the average maximum equivalent-strain induced,there exists a descending-order:quasicrystal(77%) > diamond(75%) > alumina(45%).The fatigue wear originated from plastic deformation may account for the wear-mechanism of stainless steel.