A mathematical and physical model for flow instability in one dimensional parallel rectangular channels was established, including the entrance section, heater section and riser section, and the code for flow instability in parallel two-rectangular channel was developed based on the mathematical model, which was validated with the experimental results of flow instability. Based on the code, the effect of the system pressure, the inlet and outlet throttling on the margin of stability and the frequency of oscillations was analyzed. The results showed that the margin of stability and the distribution of frequency were overlapped at different system pressure and the system would be stabilized and the frequency of the system would increase with the increasing of the inlet throttling and system pressure and the decreasing of outlet throttling.