We demonstrated the operation of cw diode-pumped Yb:YAG laser in radial or azimuthal polarized (RP or AP) beams using a combination of birefringent uniaxial crystal (c-cut YVO4 or α-BBO) and lens as intra-cavity elements. RP and AP doughnut modes (M2 = 2-2.5, polarization extinction ratio 50-100:1) with output power up to 60 mW were generated. Apart from doughnut modes, RP or AP ring-like off-axis oscillations and multi-ring beams with mixed RP and AP were also observed at the output of this laser scheme. Using intra-cavity short focus lenses with spherical aberrations AP or RP modes of higher orders was obtained. Mechanism of mode selection in the laser is discussed. The large variety of beams with axially symmetric polarizations from the output of the proposed laser scheme may find applications in different fields.