Flywheel rotor performance monitoring and damage detection are increasingly gaining the interest of manufacturers of aircraft engines. This is primary due to the fact that there is a necessity for improving safety during operation as well as a need for lower maintenance costs. Applied techniques for damage detection and health monitoring of rotors are essential for engine safety, reliability and life prediction. Preliminary design of such a flywheel studied here is based on a simple model of annular rotating disk with stress-free boundary conditions. In addition to the critical rotational speed, the paper analyses the influence of the leading design parameter - material plastic anisotropy - on the development of plastic zone and stress/strain distributions.