Influence of local voids on flow maldistribution in randomly packed fiber bundles is examined by Voronoi tessellation. A theoretical expression for the local void distribution caused by random placement of fibers is developed by using a random-cell model. Simulations and packing experiments have been conducted to assess the accuracy of the theoretical distribution of cell sizes. In the case of shell side, laminar flow parallel to the fibers, the theoretical distribution is used to estimate fRe (friction factor times Reynolds number) and volumetric flows, and to compare results with ordered arrays and experimental data from literature. The results are used to assess the contributions of local voltage variations to flow bypass. This has implications for the prediction of pressure drop and heat and mass transfer in hollow-fiber module applications where transport is dominated by flow on the shell side.