A fuel cell anode flow field includes at least one flow channel with a cross-sectional area that varies along at least a portion of its length. In some embodiments, the channel width decreases along at least a portion of the channel length according to a natural exponential function. This type of anode flow field can improve performance, reduce fuel consumption and/or reduce detrimental effects such as carbon corrosion and catalyst degradation, thereby improving fuel cell longevity and durability. When operating the fuel cell on either a substantially pure or a dilute fuel stream, this type of anode flow field can provide more uniform current density. These flow channels can be incorporated into reactant flow field plates, fuel cells and fuel cell stacks.