In this paper, based on the law of conservation of electromagnetic energy, a model of equating the electromagnetic anisotropic medium to be the electromagnetic isotropic medium is established, and its correctness is verified. Under the condition of the electromagnetic wave length being comparable to the geometrical parameters of the cylinder,the equivalent permittivity of the cylinder of gypsum crystal in the elliptical Gaussian beam varies with its geometrical parameters, beam parameters and beam propagation direction are studied. The simulation results show that the equivalent permittivity fluctuated changes with the increase of the radius of the cylinder, and the change of the equivalent permittivity is very small with the increase of the length of the cylinder. In addition, the analytical expression of the scattered field of an anisotropic cylinder being irradiated by an electromagnetic wave beam with an arbitrary direction is presented. The simulation results show that the radius of the cylinder and the angle between the electromagnetic wave propagation direction and the symmetry axis of the cylinder have a great effect on the scattering, and the length of the cylinder, the distance between the beam and cylinder and the beam waist width etc. have little effects on scattering.