The paper describes a simple, semi-analytic technique for modelling contaminant transport through the fractured till, including consideration of diffusion of contaminants from the fractures into the till matrix, sorption, and radioactive decay. The model also considers the finite mass of contaminant and dilution due to the flow of groundwater in the aquifer. The model can be readily implemented on a microcomputer. The model allows examination of variations in fracture spacing, fracture opening size, thickness of the fractured zone, diffusion coefficient, dispersivity, effective porosity of the matric, radioactive decay, Darcy velocity, thickness of the aquifer, distribution coefficient, and mass of contaminant. Results of a limited parametric study inter alia examines the effects of uncertainty in fracture spacing, the thickess of the fractured till, and the effective porosity of the till matrix. -from Authors