Fully resolved simulations of the flow through a fixed bed of pellets are performed to better understand the effect of the local microstructure on the energy loss, i.e., pressure drop through the bed. Both mono-disperse and poly-disperse systems as well as spherical and cylindrical pellets (solid particles) are investigated. Using a DEM-DLM/FD simulation method inspired by “Wachs, A. (2009). A DEM-DLM/FD method for direct numerical simulation of particulate flows: sedimentation of polygonal isometric particles in a Newtonian fluid with collisions. Comput. Fluids 38(8), 1608–1628” and implemented here in a Finite Volume context with second order reconstruction of the particle boundary as in “Rahmani, M., Wachs, A. (2014). Free falling and rising of spherical and angular particles. Phys. Fluids 26, 083301”, we evidence that the computed solution converges nicely with mesh refinement and provide guidelines on the grid size to guarantee a satisfactory level of accuracy. Based on these trustworthy simulation results, we investigate the impact of the particle shape as well as the degree of poly-dispersity in the system on the pressure drop over the fixed bed in the viscous regime. Unprecedented simulation results on the flow through a bed of poly-disperse cylinders indicate that the correlation for poly-disperse spheres suggested in “Van der Hoef, M.A., Beetstra, R., Kuipers, J.A.M. (2005). Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233–254” may still be valid for cylinders of moderate aspect ratio.