The couple stress of a three-dimensional vertical granular ow is investigated by means of a combined approach of discrete element method and averaging method. The velocity, mass density and couple stress are quantiΓΏed under various ow conditions. The velocity and mass density proΓΏles are illustrated to be consistent with those obtained by the previous experiments and numerical simulations, conΓΏrming the validity of the proposed approach. The couple stress proΓΏles are shown to be signiΓΏcantly a ected by the wall supporting the vertical ow, and be contributed by the rolling resistance due to the asymmetrical normal traction distributions in the contact areas between particles and between particle and wall. For mono-sized particles, the couple stress far from the wall can be ignored although it may vary slightly causing the uctuation of ow behavior; however, the couple stress in the region close to a wall must be taken into account to properly describe the ow behavior of particles. For multi-sized particle, the couple stress is mainly contributed by the sliding resistance and to a less degree by the rolling resistance; the transport of particle plays a limited role. Implication of the present numerical results to continuum modeling is also discussed.