Instabilities associated with the operation of liquid rocket propulsion systems and test facilities usually manifest themselves as structural vibrations and may cause structural damage. While the source of the instability is directly related to the performance of a component such as a turbopump, the associated pressure fluctuations as they propagate through the system have the potential to amplify and resonate with natural modes of the system. In this proposal, a novel multi-level (system and component) instability analysis tool is proposed to identify these resonant modes. In Phase I of this program, a Transfer Matrix based approach was developed to analyze the propagation of an instability through a limited range of components such as ducts, bends, orifices and diffusers. The initiation of an instability was resolved with the help of high-fidelity CFD simulations. Demonstration of the tool was successfully carried out for the propagation of an instability in a scaled down system. In Phase II, the tool will be expanded to include a wider array of components such as turbopumps, valve systems etc. This will permit analysis of a greater range of instabilities from multi-phase instabilities involving cavitation based events in turbopumps to valve based instabilities such as water hammer.