Small Modular Reactors (SMRs) can be utilized as small-scale distributed power sources at a lower cost than large-scale commercial nuclear power plants, thus various types of SMR development are underway worldwide. Among them, the SMR with natural circulation cooling even at full power has the advantage of improving the compactness and safety, but it requires an additional heat source at the initial start-up because the coolant pump cannot be used for heating and pressurizing the system. It was previously identified that flow instability can occur due to unbalanced heating between the heated flow channels under natural circulation. Therefore, if the natural circulation flow is formed and pressurized using only the core power the investigation of the flow instability becomes imperative. This is because the flow instability can cause mechanical vibrations, disturb the control system and cause instability of system operation. In this thesis, the instability occurring as a flow reversal phenomenon, which can occur at the initial start-up using only the core power, was studied. After examining the flow instability that can occur in the existing simple multiple parallel-channel system, the conditions that can induce instability in the multiple parallel-channel under the similar environment as the SMR operating conditions were evaluated.