This paper describes a computer simulation study of brittle particle attrition in a shear cell in two dimensions. The results obtained indicate that the rate of attrition is directly related to the total amount of work performed on the system, including the initial work required to accelerate and expand the bed. These results seems to be in general agreement with the results of similar experiments performed in three dimensions for some materials. The results indicate that experimental errors may arise from the inertia of the movable plate of the shear cell.