The Discrete Element Method (DEM) simulations are performed to investigate shear flows of polydispersed, cylindrical particles. Binary mixtures and Gaussian distribution mixtures are considered in the simulations to study the effect of polydispersity on the rheology and particle phase stresses. It is observed that no segregation occurs in the shear flows in the absence of gravity and interstitial fluid medium and the orientational alignment of a particle species in a mixture is affected by the interaction with other species. The stresses of a binary mixture are bounded by those of the monodispersed systems of two particle species. The minimum stress difference due to the change in volume fraction of a particle species, i.e. the minimum effect of polydispersity, is observed at the solid volume fraction of 0.2. For the Gaussian distribution systems with the same average particle aspect ratio, the effect of standard deviation of particle aspect ratio on the stresses is limited. A model that accounts for the effect of particle species concentration is eventually proposed to evaluate the stresses of the polydispersed, cylindrical particle flows. In the model, the stress tensor of the polydispersed system is expressed as a sum of the stress tensors of the monodispersed systems of all the particle species, which are linearly scaled by the volume fractions of the corresponding species in the mixture. The model predictions are in good agreement with the DEM simulation results for the binary and Gaussian distribution mixtures. (C) 2019 Elsevier B.V. All rights reserved.