This paper concerns a method and a test set-up to measure the permeability of plates of metal foams and sets of wire meshes used to control flows in fluid filters and other flow systems designed to yield constant velocity distributions over large cross sections of flows. The method is based on permeability considerations using the Ergun equation to describe the pressure losses of packages of mono-dispersed spheres. One correlation is suggested for the permeability k over the entire range of mean velocities U0. A suitable measuring set-up was designed, built and used to measure the permeability of plates of metallic foams and sets of wire meshes. The specific objective of the present investigation was to provide permeability data for combined sets of wire meshes with flow properties that are mainly characterized by the wire meshes with the smallest mesh size. A method of data presentation is suggested that clearly illustrates the ranges of laminar and turbulent flows through the wire meshes. The results are compared with those for technical porous plates. The suggested presentation of the results indicates that the general features of the flows through porous plates of metal foams and wire meshes are the same.