This letter presents a novel robotic manipulation technique that we call robotic edge rolling. It refers to transporting a cylindrical object by rolling on its circular edge, as human workers might maneuver a gas cylinder on the ground. Our robotic edge rolling is achieved by controlling the object to both roll on its bottom edge in contact with the ground and slide on the surface of the robot's end effector. It can thus be regarded as a form of robotic dexterous, in-hand manipulation with nonprehensile grasps. We address the problem of grasp planning for edge rolling by studying how to design appropriately shaped end effectors with zero internal mobility and how to find feasible grasps for stably rolling the object quasi-dynamically with our simple end effectors. An extensive set of experiments is performed with a conventional manipulator arm on not only flat surfaces but also a U-shaped half-pipe track. Long-range edge rolling is demonstrated with a modular mobile manipulator that is capable of active steering control.