Carbon nanofiber (CNF) nanopaper has shown great potential to improve the surface of fiber reinforced polymeric composites, including providing EMI shielding and erosion resistance. During typical Resin Transfer Molding process (RTM), the CNF nanopaper is incorporated into fiber preform as a surface layer. In order to learn how resin flows through the fiber preform and nanopaper layer, permeability of fiber preform and nanopaper need to be measured. As is well known measuring permeabilities of fiber preforms is a very difficult experimental task. Results are usually with large experimental variability. Measuring permeabilities of nanopapers is even more complicated. Therefore, in our group, permeability of carbon nanofibers based nanopapers was measured using different experimental set ups to improve accuracy of results. In plane permeability of nanopaper was measured by both 1D and radial flow approaches. Thru plane permeability was measured as well, using a flow cell and flow visualization experiments. In this paper, we discuss the methods used and provide experimental results. We also conduct computational fluid dynamic simulations to study the detailed flow patterns of the RTM process and compare with experimental measurements.