The problems of the anisotropy of both scattering and fission and of its effects on mono-energetic neutron flux distributions are discussed for both plane and spherical symmetries. After a statement of the problem for the case of a general anisotropy, the case of a finite-order anisotropy with azimuthal symmetry is considered, and various quantities of interest are studied as a function of a parameter that appropriately accounts for the different anisotropic behaviors of scattering and fission. Numerical results for the linearly anisotropic critical case in both plane and spherical symmetries are reported and are completed with the ones obtained by asymptotic method.