In the design stage or analysis of any dynamical system a detailed or comprehensive model is essentially required. In this work, different parts and components that are contained in the model of a turbo-generator unit (T.G) for torsional vibration analysis are considered and the governing equations of which are presented and developed to estimate their respective parameters. These parts and components are mainly compressor seventeen stages and blades, turbine two stages and blades, reduction gear system with the safety shaft, the rotor of the generator, the exciter and the fluid film bearings on which the whole system is supported. The data upon which the system model is built are referred to Mosul gas turbine station units.The estimated parameters are those related to rotational inertia, damping and stiffness effects of the different components in the system.A detailed model of the system should be useful for the purpose of torsional vibrational during rotation with normal steady loading or under severe loading conditions utilizing a block diagram via Matlab. The system eigen values natural frequencies (critical speeds) and mode shapes are determined.