We study the influence of the anisotropic white matter within the ElectroEncephaloGraphy source localization problem. To this end, we consider three cases of the anisotropic white matter modeled in two concrete cases: by fixed or variable ratio. We extract information about highly anisotropic areas of the white matter from real Diffusion Weighted Imaging data. To validate the compared anisotropic models, we introduce the localization dipole and orientation errors. Obtained results show that the white matter model with a fixed anisotropic ratio leads to values of dipole localization error close to 1cm and may be enough in those cases avoiding localized analysis of neural brain activity. In contrast, modeling based on the anisotropic variable rate assumption becomes important in tasks regarding analysis and localization of deep sources neighboring the white matter tissue.