The sedimentation of a rectangular particle in a two-dimensional channel filled with viscoelastic fluid was simulated by using finite element arbitrary Lagrangian-Eulerian domain method. The stable orientation of a rectangular particle for different elasticity numbers was obtained, and the effects of aspect ratio and blockage ratio on the settling characters were also discussed. Results show that there is a critical elasticity number when a rectangular particle falls in a viscoelastic fluid. When the elasticity number is smaller than critical, the stable orientation is that the long side of the particle perpendicular to gravity. For larger elasticity number, the stable orientation is that the long side of the particle parallel to gravity. Aspect ratio and blockage ratio have great effects on the particle's settling behavior. Both the fluctuations of the orientation and lateral drifting distance increase with increasing aspect ratio, while decrease with increasing blockage ratio. Settling velocity decreases with increasing aspect ratio, but increases with increasing blockage ratio. The critical elasticity number is a decreasing function of aspect ratio, and is an increasing function of blockage ratio.