A description of macroscopic pore structure is discussed in regards to fluid flow through a porous media. Using volume and area averaging procedures for relative fluid flow, an anisotropic pore structure is defined by two parameters: the volume porosity and the second order structural permeability tensor. Such a characterization allows for a consideration of the fluid flow described by the volume average velocity as the superposition of three one-dimensional flows at the area average velocities along mutually perpendicular directions. This also leads to the understanding that only part of the fluid can flow unimpeded while the rest is trapped in the porous skeleton.