A Monte Carlo study is conducted to examine the joint influence of aperture variability and rheological parameters on non-Newtonian flow in a single fracture. The aperture field is generated stochastically and the flow problem is solved under the lubrication approximation. Three fluid rheologies (Newtonian, power-law and Carreau) are considered to ascertain the impact of the rheological law on the effective flow parameters. Extensive simulations over large statistics of fractures allow determining the uncertainty associated with the prediction.