This paper describes an approximate method for analyzing two-phase flow of gas and liquid water in fuel cell channels, whose surfaces are sufficiently hydrophilic for liquid water to wick spontaneously into the channel corners. This analysis is used to address the important question of whether the gas flow at typical stoichiometries in such channels is sufficient to remove all the liquid water generated in a proton exchange membrane fuel cell. Since fuel channels are usually much narrower than they are long, it is possible to adopt the usual approximations of lubrication theory and to decompose the general solution for the liquid motion into two parts: (1) that driven by the channel pressure gradient and (2) that driven by surface shear stress from the faster moving gas. When both parts of the solution are combined with the mass balance equations, it is possible to derive a pair of partial differential equations for the water depth and gas flow rate that depend on distance down the channel and time. Steady solutions of these equations are explored to determine the amount of liquid water that accumulates in the channel over a broad range of fuel cell operating conditions.