In relation to the cooling system of high performance microelectronics, a high power research reactor with plate type fuels and plasma facing components of a fusion reactor, study of two-phase flow in a narrow rectangular channel has been paid considerable attention, recently. For the two-fluid model, direct geometrical parameters such as the void fraction should be used in flow-regime criteria. From this point of view, flow-regime transition criteria for vertical upward flows in narrow rectangular channels have been developed considering the mechanisms of flow-regime transitions. The basic concept of the present modeling followed the Mishima and Ishii model for vertical upward two-phase flows in round tubes. Newly developed criteria have been compared with the existing experimental data for air-water flows in narrow rectangular channels with the gaps of 0.3-17 mm. The present criteria showed satisfactory agreements with those data. Further comparisons with data for steam-water in a rectangular channel at relatively high system pressures have been made. The results confirmed that the present flow-regime transition criteria could be applied over wide ranges of parameters as well as to boiling flow.