Are humans able to perceive the circularity of a cylinder that is grasped by the hand? This study presents the findings of an experiment in which cylinders with a circular cross-section had to be distinguished from cylinders with an elliptical cross-section. For comparison, the ability to distinguish a square cuboid from a rectangular cuboid was also investigated. Both elliptical and rectangular shapes can be characterized by the aspect ratio, but elliptical shapes also contain curvature information. We found that an elliptical shape with an aspect ratio of only 1.03 could be distinguished from a circular shape both in static and dynamic touch. However, for a rectangular shape, the aspect ratio needed to be about 1.11 for dynamic touch and 1.15 for static touch in order to be discernible from a square shape. We conclude that curvature information can be employed in a reliable and efficient manner in the perception of 3D shapes by touch.