Natural circulation systems are prone to several types of flow instabilities under some of the operating conditions. A reliable prediction of stable and unstable operating regimes is of paramount importance for successful deployment of these systems. In the present stud, a system analysis model, based on HEM approach has been developed and a semi-implicit scheme with adaptive time step has been used to solve the governing equations. The proposed numerical scheme predicts the system stability behaviour adequately for a wide range of nodalizations, a key requirement for analysis of natural circulation based systems. Paper describes the mathematical model and its application to single-channel natural circulation systems. The mechanism for type-I and Type-II density wave oscillation has been discussed.