Motion of a rectangular particle in a two-dimensional vertical shear flow of Newtonian fluid and viscoelastic fluid with different parameters is studied using the finite element arbitrary Lagrangian-Eulerian domain method.The results show that the centerline of the channel is a stable equilibrium position for the neutrally buoyant rectangular particle in a vertical shear flow.Inertia causes the particle to migrate towards the centerline of the channel.In addition, a critical elasticity number exists.When the elasticity number is below the critical value,the rectangular particle migrates to the centerline; otherwise the centerline of the channel is apparently no longer a global attractor of trajectories of the particle.