The Tabor friction model was modified by introducing the friction factor. Based on the multi-region model, the micro-uniaxial compression process was simulated to study the size effect considering dry friction. It was found that the grain-boundary has little effect on the dry friction behavior. The mechanical properties of individual grains either in the contact area or in the non-contact area have a significant influence on the friction behavior. With decrease of specimen's size, the average friction coefficient did not vary much but the value of friction coefficient of each random grain orientation distribution becomes more dispersive. (C) 2012 Elsevier Ltd. All rights reserved.