A stochastic model for the calculation of flow and contaminant transport in a single fracture with variable apertures was presented. The spatially varying apertures of the fracture were generated using a geostatistical method, based on a given aperture probability density distribution and a specified spatial correlation length. Fluid flowed between two points in the fracture plan. The fluid potential at each node of the discretization mesh was computed and the steady state flow rates between all the nodes were obtained. Then the contaminant transport was calculated using a particle tracking method. The migration plumes of contaminant between the inlet and the outlet were displayed in contour plots and contaminant elution profiles were also plotted. Calculations showed that fluid flow occured predominantly in a few preferred paths. Hence, the large range of apertures in the fracture gives rise to flow channeling. Simulation results were correlated with the basic input parameters : standard deviation of a lognormal aperture distribution function and the spatial correlation length.