quantization of electromagnetic field in the presence of an anisotropic polarizable and magnetizable medium, we model the medium by two independent reservoirs. Each reservoir contains a continium of three dimensional harmonic oscillators labeled with a continuous parameter $\omega $. We call these two continuous sets of oscillators “$E$ field ” and “$M$ field”. The $E$ field and $M$ field describe polarizability and magnetizability of the medium, respectively. This means that, in this approach it is not needed the electric and magnetic polarization fields of the medium to be appeared explicitly in the Lagrangian of the total system as a part of the degrees of freedom of the medium , but the contribution of the medium in the Lagrangian of the total system is related only to the Lagrangian of the $E$ and $M$ fields and these fields completely describe the degrees of freedom of the medium. The presence of the “$E$ field” in the total Lagrangian is sufficient for a complete description of both polarizability and the absorption of the medium due to its electrically dispersive property. Also the “$M$ field” solely is sufficient in order to description of both magnetizability and the absorption of the medium due to its 