AbstractA formulation is developed for the flow of an incompressible fluid through a two dimensional packed bed having a spatially variable void fraction, through the statement of the Ergun Equation in a two dimensional system.Computed results are presented for particular spatially distributed void fractions in the bed, which indicate that a lateral variation in the resistance to flow may cause appreciable flow maldistribution and “cross flow” effects.This work is thought to be a first, necessary step in the quantitative understanding of channeling and by‐pass phenomena in packed bed rea