We present EUgran + Poly, an augmentation of the numerical hybrid model EUgran+ (Pirker et al., 2010, Powder Tech. 204, 203-213), an Eulerian-Eulerian granular phase model extended with Eulerian-Lagrangian discrete phase approaches for rapid granular flows, with the ability to handle poly-dispersed dilute and dense particle-laden flows. Our modifications include (a) the implementation of a new poly-dispersed drag law and of (b) new boundary conditions distinguishing between sliding and non-sliding particle-wall collisions using (c) the adaptions of the Eulerian-Eulerian granular phase by Schneider-bauer et al. (2012a. Chem Eng. Sci. 80, 279-292). The EUgran+ Poly model was validated using three specific cases with different mass loadings: (i) poly-dispersed particle-laden flow in a square pipe with a 90 degree bend at low mass loading (L=0.00206); (ii) particle-laden flow in a rectangular pipe with a double-loop at high mass loading (L=1.5); (iii) poly-dispersed dust separation in a cyclone with mass loading (L=1). The results show that incorporating a poly-dispersed phase significantly improves the accordance between simulation results and measurements. Our hybrid model provides substantial savings in terms of computational effort and cost while maintaining satisfactory simulation quality. (c) 2013 Elsevier Ltd. All rights reserved.