•A two-dimensional model for the design of flow fields in VRFBs is reported.•Uniformity of vanadium ion distribution is evaluated by uniformity factors.•Pressure drop is accurately captured in interdigitated and serpentine flow fields.•Performance of several design of flow fields for a large cell is studied. In this work, we report a two-dimensional mathematical model for the design of flow fields in vanadium redox flow batteries (VRFBs). The model is validated by calculating the pressure drop, distribution uniformity of vanadium ions in an interdigitated flow field and a serpentine flow field for a 9-cm2 cell. The model is then used to simulate interdigitated and a series of parallel serpentine design of flow fields in a 410-cm2 cell. It is demonstrated that with an increase in the number of parallel serpentine channels, the pumping power decreases while the distribution of vanadium ions becomes less uniform. Among the design of flow fields studied in this work, the interdigitated design performs the lowest pumping power and the most uniform distributions of vanadium ions.