The theory of flow similarity has not been well established for granular flows, in contrast to the case for conventional fluids, owing to a lack of reliable and general constitutive laws for their continuum description. A rigorous investigation of the similarity of velocity fields in different granular systems would be valuable to theoretical studies. However, experimental measurements face technological and physical problems. Numerical simulations that employ the discrete element method (DEM) may be an alternative to experiments by providing similar results, where quantitative analysis could be implemented with virtually no limitation. In this study, the similarity of velocity fields is investigated for the rolling regime of rotating drums by conducting simulations based on the DEM and using graphics processing units. For a constant Froude number, it is found that the particle-to-drum size ratio plays a dominant role in the determination of the velocity field, while the velocity field is much more sensitive to some material properties than to others. The implications of these findings are discussed in terms of establishing theoretical similarity laws for granular flows. (C) 2015 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.