Abstract: In this paper, the finite element method (FEM) is applied to analyze the electromagnetic scattering of the complex media targets, such as the anisotropic media biisotropic media and bianisotropic media. The general FEM functional formulation of linear media is built, and the specific expression of the FEM matrix equation is derived. This FEM functional formulation is applicable for the bianisotropic media, and for the anisotropic or biisotropic media as well. In order to demonstrate the accuracy and generality of the developed FEM, we calculate some scattering from the ferrite sphere, chiral sphere, plasma sphere and Ω media target. The numerical results are in agreement with the published data.