The migration of deep-well injected waste in heterogeneous confining layers is evaluated using numerical simulation. Of primary concern is the migration potential through permeable sand paths between less permeable shale. The configuration of the predominantly shale confining layers was defined by Monte Carlo techniques assuming a binary random structure composed of pure sand and pure shale. Three-dimensional flow simulations using Modflow, a finite difference model, indicated that essentially continuous sand paths and unacceptably rapid transport might exist through confining layers with an average shale fractions of less than about 0.65 and that two and three dimensional flow simulations were essentially equivalent for high (>0.6-0.7) or low (<0.4-0.5) shale fractions. Diffusion and advection-dispersion in the configurations with a shale fraction greater than 0.65 were estimated via a two-dimensional finite element model. Interaction between organic constituents of the waste and the soil media is represented by linear sorption. The model was applied to an example in which dilute aqueous solutions of acrylonitrile were deep-well injected. Advective penetration of a representative confining layer over 10,000 years was found to be small (<3 m assuming injection pressures were maintained throughout the period). Even including diffusion and dispersion, concentrations in excess of drinking water criteria did not extend beyond the confining layers after simulation for 10,000 years.