Breccia is a lithologicat facies present in the McMurray Formation in the Athabasca region of northeast Alberta. It consists of mud or shale clasts embedded in clean sands. The mud content of this facies varies from 0 to 100% and the clasts range in size from millimetres to metres with varying degree of angularity and sorting. Breccia is common in bitumen reservoirs. From an in situ recovery perspective, breccia can impede fluid flow and reduce the overall oil saturation due to the presence of the mud clasts. To properly characterize the reservoir flow properties, it is necessary to develop a systematic procedure to capture the impact of these clasts to a scale that is suitable for numerical flow simulation. This is commonly referred to as upscaling in reservoir characterization. The procedure described here involves digitizing core photographs of breccia intervals and assigning a sand-mud facies indicator based on the presence or absence of mud clasts at the pixel level of the core photograph. The resulting indicator map is transferred to a numerical flow simulator. The 2D effective permeability of the breccia zones is determined numerically from single-phase flow simulations by assigning a constant permeability to the sand and zero permeability to the mud clasts. The results indicate that breccia permeability closely follows an averaging power law in terms of the mud content. A 2D mathematical theory is developed to calculate the permeability of breccia facies by treating the mud clasts as elliptic obstacles to the flow through the embedding sand of known permeability. The results from the theory are shown to be in satisfactory agreement with those from the flow simulation. The paper concludes with guidelines for systematic permeability assignment in the breccia zones of oil sands, as well as other similar formations.