Vibration is one of the primary concerns in rotating machinery. Vibration reduction will help extend turbo-machinery life and is viewed as one of the major winning points for turbine-generator (T-G) manufacturers. To better predict the level of machine vibration requires a great deal of analysis. The success of different analyses mainly rely on reliable models that are accurate and consistently verifiable by testing. Towards this objective, many researchers and businesses spent enormous amount of time and money in the development of accurate and reliable models that closely simulate reality. However, research in rotor dynamic modeling is an on-going effort. In this paper, another new modeling approach that uses strain energy is reported. This modeling technique was successfully applied for rotor torsional and lateral analyses with greater accuracy. Further, a faster and more stable solution method which uses Riccati algorithm is discussed.