In microchannel flow, gas-liquid interface behavior is important for developing a wide range of microfluidic applications, especially in passive microfluidic systems. This paper presents a discussion of interface motion driven by capillary action in a microchannel. We have extended the theory beyond the previous theory of capillary rise problem for a circular tube, to a rectangular microchannel. The same formula for the relation between nondimensional time and interface position is obtained as for a circular tube. We examined rectangular microchannels with several sizes (about 50 to 100 microm square) of glass capillaries and 85 x 68 microm and 75 x 45 microm polydimethylsiloxane (PDMS) microchannels fabricated by photolithography technique, respectively. We observed movement of the gas-liquid interface position and compared it to the dimensionless relation. We obtained the value of a dimensionless variable of driving force that is related to dynamic contact angles for glass-water, glass-ethanol, and PDMS-ethanol. Using this variable, interface motion can be predicted for any size of rectangular channels.