Non-Darcy flow occurs in the near-wellbore region of high-capacity gas and condensate reservoirs. Forchheimer's equation describes this flow in isotropic media. Many naturally occurring porous media are, however, anisotropic. This study is directed at understanding the non-Darcy flow behavior in porous media that are anisotropic at the port-scale. Three structural models of anisotropy are proposed: size-induced, connectivity-induced and spatial correlation-induced. Non-Darcy flow has been computed in these netwoks, as well as the tortuosity and porosity of the media. A tensorial form of the Forchheimer equation has been proposed and verified. The non-Darcy term has been found to be tensorial and proportional to the square of the superficial velocity at the macroscopic scale. As the pore-scale anisotropic parameter increases, non-Darcy and tortuosity components increase, but permeability components decrease. An approximate correlation is derived between the non-Darcy coefficient, the permeability, and the tortuosity tensors.