Circular core fibers have been gradually replaced with polygonal core fibers in the high-precision radial velocity measurement systems. Further, the scrambling schemes combining polygonal fibers, lenses, or circular fibers have been subsequently proposed. This study simulated the scrambling properties of circular and octagonal fibers together with the double-fiber scrambler based on these two fibers using the ray tracing method. The simulation results show that although circular fibers have good angular scrambling properties in both the far and near fields, their radial scrambling properties are not good. For octagonal fibers, the near field scrambling is better than that of circular fibers, whereas their far field scrambling is not obviously different from that of circular fibers. A double-fiber scrambler can effectively improve the fiber scrambling performance. In addition, a double-fiber scrambler with octagonal fibers exhibits excellent scrambling performances in both the far and near fields.