AbstractThis paper presents a non‐equilibrium sorption dispersion–advection transport model for the analysis of pollutant migration through soil. The formulation involves a convolution integral of the product of the rate of change of concentration and a time‐dependent sorption coefficient, suggesting an integral transformation of the governing equations. This facilitates the primary purpose of this paper, to incorporate a time‐dependent solute sorption process into a computationally efficient and accurate semi‐analytic Laplace transform method. An application of the non‐equilibrium sorption model for backfiguring dispersion–advection equation parameters from experimental data is presented, and the implications of non‐equilibrium sorption on the design of landfill liners is explored by means of an illustrative example.