An energy storage system is generally disclosed. An example system includes a flywheel having a substantially cylindrical flywheel portion, and a housing defining a substantially cylindrical cavity configured so as to receive the substantially cylindrical flywheel portion. The flywheel is rotatable in the cavity about a central axis of the flywheel, and an energy exchange device is configured to convert between electrical energy and kinetic energy associated with rotation of the flywheel. The system may also have a magnetic restraint arranged to exert a magnetic restraining force on the flywheel in a direction towards the central axis.