A stability analysis of a Row boiling two-phase low pressure and downflow system relative to the occurrence of critical heat flux has been carried out. The problem formulation is based on a time and area averaged one-dimensional drift flux model, with the necessary constitutive equations. A characteristic equation is obtained to predict the onset of flow excursion and density wave oscillations. By non-dimensionalizing the characteristic equation, important groups governing the system stability are determined, The results of the analysis are useful in determining the region of stable operation for downflow in the Westinghouse Savannah River Site Reactor and in avoiding the onset of Row excursions and density wave oscillations. The analytical results for flow excursion are compared with the Babcock and Wilcox flow excursion experimental data with a Savannah River Mark 22 fuel assembly mockup.