An exponential finite-element model for multiple-porosity contaminant transport in soils is proposed. The model combines three compartments for dissolved contaminants: a primary compartment of diffusion.advection transport with nonequilibrium sorption, a secondary compartment with diffusion in rectangular or spherical soil blocks, and a tertiary compartment for immobile solutions within the primary compartment. Hence the finite-element model can be used to solve four types of mass-transfer problems which include: (1) intact soils, (2) intact soils with multiple sources of nonequilibrium partitioning, (3) soils with a network of regularly spaced fissures, and (4) structured soils. Hitherto, mobile/immobile compartments, fissured soils, and nonequilibrium sorption have been treated separately or in pairs. A Laplace transform is applied to the governing equations to remove the time derivative. A Galerkin residual statement is written and a finite-element method is developed. Both polynomial and exponential finite elements are implemented. The solution is inverted to the time domain numerically. The method is validated by comparison to analytical and boundary element predictions. Exponential elements perform particularly well, speeding up convergence significantly. The scope of the method is illustrated by analyzing contamination from a set of four waste repositories buried in fissured clay.