We consider a vector cylindrical polarized beam having a symmetric transverse distribution of the amplitude of the electric field vector of the electric field relative to the axis, incident on planar inhomogeneous anisotropic layer. The beam is presented in the form of a set of plane polarized waves. For each of the waves, based on Maxwell's equations, a matrix solution is obtained for a wave propagating in a gyrotropic medium, as well as a reflection and transmission matrix. The transmitted and reflected beams are restored by the inverse Fourier transform.