A model of the unidirectional consolidation of a clay soil or flocculated suspension between a series of parallel drains is developed. A convective-diffusion equation for the pore pressure is derived, and an equal-strain approximation leads to an expression for the average effective stress profile between the drains. The solution depends on a Peclet number quantifying the ratio of the bulk soil flow rate to the rate of consolidation. By adjusting the number, height and spacing of the drains, very high rates of dewatering can be achieved. A potential application of the method to the rapid dewatering of mine tailings is described.