In the present paper,from the second order partial differential equations for solving the magnetotelluric(MT) fields of general anisotropic medium,we first obtained the second order partial differential equations for some anisotropic media with special conductivity(e.g.diagonal anisotropy,transverse anisotropy,azimuthal anisotropy,etc.) by simplifying the electrical conductivity tensor of anisotropic medium.And then we obtained the analytic solutions to MT fields for the case of transverse and azimuthal anisotropy through converting the conductivity parameter based on that of diagonal anisotropy.We further discussed the influence of the selection of integral limit and step length on precision in solving the analytic solutions for MT fields of isotropic medium.Finally,we presented the MT responses of two transverse and azimuthal anisotropic media as well as some applications of the analytic solutions to MT fields of anisotropic medium. In the present paper, from the second order partial differential equations for solving the magnetotelluric (MT) fields of general anisotropic medium, we first obtained the second order partial differential equations for some anisotropic media with special conductivity (egdiagonal anisotropy, transverse anisotropy, azimuthal anisotropy, etc.) by simplifying the electrical conductivity tensor of anisotropic medium. And then then obtained the analytic solutions to MT fields for the case of transverse and azimuthal anisotropy through converting the conductivity parameter based on that of diagonal anisotropy. further proceeded the influence of the selection of integral limit and step length on precision in solving the analytic solutions for MT fields of isotropic medium. Finally, we presented the MT responses of two transverse and azimuthal anisotropic media as well as some applications of the analytic solutions to MT fields of anisotropic medium.