The dissertation discusses the calculation and design of flywheel energy storage systems with electromechanical power converters and composite-fibre flywheels. For this purpose, the main load criteria for centrifugal and pressure loads on flywheel rings of unidirectional laminates are determined, and criteria are given for the dimensioning of flywheel rings. The fast rotational speed of the flywheel dominates the design of the driving motor. As an example, the calculation of a permanent-magnet-excited external rotor motor is described. Special consideration is given to the close correlation between stator current density and ampere bars per cm, and rotor strength. The findings are illustrated by design examples, by an example from the field of vehicle construction, and by experimental studies on composite-fibre flywheels and a driving motor with a high rotational speed.