The drag properties of flow through and around square arrays of 10 x 10 evenly spaced circular cylinders with a wide range of solid fraction phi from 9.69 x 10(-11) to 0.785 and Reynold number of the array Re from 1 to 50 are investigated numerically. The purpose of the present study is to better understand the phenomena of flow through and around permeable bodies that appear in bioreactors and fluid-solid reactors, for example. Instead of using the semi-empirical porous medium model, the direct numerical simulation is employed in order to investigate the flow mechanism from a microscopic point of view. A peak in drag coefficient is observed for the range of phi investigated, which appears at a smaller phi as Re increases. Three flow regimes are identified based on the shape effects quantified via the averaged velocity within the array, and the drag property in each regime is analyzed. A novel drag formula is also found by investigating the dependence of drag on phi and R (Reynolds number based on the mean velocity within the array). Finally, the dimensionless macroscopic permeability Da is estimated via the Darcy's law. The drag ratio computed is in a good agreement with the previous results from porous media models. (C) 2019 Elsevier Ltd. All rights reserved.