In order to clarify the influence of fiber shape on the motion of a fiber in non-Newtonian viscoelastic fluids, the free falling behavior of a cylindrical slender body has been experimentally investigated in stationary polymer solutions. In this paper, experimental results on the effects of body diameter and length on the falling trajectory, horizontal and vertical velocities, and variation of attitude of a slender body were reported in detail. Furthermore, the hydrodynamic mechanism of the results was discussed by considering the rheological properties of polymer solutions and introducing a supercritical flow theory. Main findings obtained from this study can be summarized as follows : (1) A slender body falling in polymer solutions rotates its attitude into horizontal direction when the diameter of a body is larger than a certain critical value. However, it turns into vertical direction regardless of its diameter in the more concentrated polymer solutions. (2) Both the horizontal and vertical velocities of a body become smaller and the final orientation angle becomes closer to vertical direction as the body diameter decreases. (3) With increasing the body length, the angular velocity of a body varies more slowly but the body adopts its final attitude closer to vertical direction. (4) As the body length increases, the translational velocities of a body become larger but the final orientation angle becomes smaller. (5) Falling behavior of a slender body can be interpreted by a new mechanism introducing a supercritical flow theory around a body and the competition between inertia and viscoelastic effects.