The generation of cylindrical vector beams in birefringent crystals is studied analytically and experimentally in paraxial and non-paraxial regimes. At sharp focusing (in the non-paraxial case), two foci corresponding ordinary and extraordinary beams are formed along the crystal’s axis. There is the radially polarized distribution in one focus and the azimuthally polarized distribution in the other focus when the incident beam has the vortex phase of the first order and circular polarization of the opposite direction. The results are extended to the generation of higher-order radially and azimuthally polarized laser beams. The physical experiments with an Iceland spar crystal have been conducted.