The mechanism of the displacement washingg of the bed of pulp fibres is mathematically modelled using a single parameter namely, Peclet number. The bulk fluid concentration is assumed to be the function of washing period and position in the bed. The effect of Peclet number on exit solute concentration is shown using the breakthrough curves. A non-linear adsorption isotherm (Langmuir) is used to describe the relationship between bulk fluid-concentration and the concentration of solute accumulated on the particle surface. The validity of the model is shown using the literature data. A comparison of washing behaviour of pulp fibres and static bed of glass beads is also presented.