Abstract: To avoid the numerical instability problems at the discontinuous points at ONB (onset of boiling) and dry out, the AEICE numerical algorithm, which is based on the EICE(extended implicit continuous fluid eulerian method), is developed. Furthermore, the AEICE is used to analyze the thermo hydrodynamic instabilities of boiling two phase natural circulation system, which may exist in the advanced nuclear reactors. It shows that increa sing system pressure or inlet subcooling can enlarge the system stability region. The numerical results correspond well with the experimental data.