With the focus on water uptake by proton exchange membrane, a two-phase, non isothermal, transient and two-dimensional model of fuel cell is developed. Further, in order to obtain the equilibrium concentration of water in the membrane, two different approaches of water-uptake by the membrane are considered; though each takes into account the Schroeder's paradox as well as individual contributions of water vapour and liquid water. Furthermore, in both the approaches, rate of water uptake is proportional to the difference between equilibrium concentration and actual concentration of water in membrane. Model results show good agreement with the experimental results. A comparative analysis of the two approaches has been presented for various results, such as liquid saturation, net drag coefficient, temperature, water content in membrane, etc. Obtained results revealed significant difference between predicted current densities, water content of membrane and temperatures for the two approaches. These differences may be reflecting the need to correctly understand water uptake by membrane and its importance for accurate modelling of fuel cell. Response in transient state of fuel cell is also studied when a step change to cell voltage is applied. Likewise, studies on rate of sorption and desorption of water by membrane explain the increase or decrease of the water content of membrane. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.