A short-focus glass lens with strong spherical aberration was used for mode selection in the cw LD-end-pumped Yb:YAG ceramic laser. Sequence of low to very high order Laguerre–Gaussian (LG pl ) modes with different combinations of radial, p and azimuthal, l indices (p⩽10, l⩽28), with output beam diameters 2–13mm and power up to 30mW was obtained. Peaked and hollow multi-ring beams with near-diffraction free propagation of the central minimum or maximum over 40m distance from the laser resonator were observed. Mechanisms of mode selection and possible applications of the proposed laser scheme are considered.