Flywheel energy storage devices may be coupled to mechanical transmissions for braking energy recovery and the provision of additional power for acceleration in hybrid vehicles. Power transmission across a continuous range of speed ratios is necessary. The flywheel size and depth-ofdischarge must be chosen for a particular application, and this has a direct effect on transmission efficiency, required gearing ratios and mass of components. Optimisation of these parameters requires a fundamental understanding of this interaction, which has not previously been investigated and reported. To address this, the current paper presents a new method of analysing mechanical flywheel systems. A simple algebraic analysis can be used to specify flywheel system parameters for any regenerative braking application where the flywheel is used to provide initial acceleration of the vehicle from stationary. This has been applied to systems using geared transmissions with continuous speed variation achieved through sliding contact in clutch and brake components. The results of the analysis highlight how the optimum selection of flywheel depth-of-discharge must achieve a balance between high transmission efficiency and low system mass. This is illustrated for a passenger car application, allowing a full assessment of system performance and the specification of appropriate design parameters.