The use of a simple short‐focus plano‐convex glass lens with strong spherical aberration for Laguerre‐Gaussian mode selection in a continuous wave (CW) LD‐end‐pumped Yb:YAG ceramic laser is demonstrated. Mode selection was obtained in a nearly meter long plane‐parallel cavity by shifting an intra‐cavity lens of 2.5 cm focal length along the resonator axis. Sequence of Laguerre‐Gaussian (LGp,l) modes with different combinations of radial (p) and azimuthal (l) indices from low to high orders (p =0–12, l = 0 – 28) with output beam diameters 2 – 13 mm and power up to 30 mW was produced. Along with many low order modes, the whole lineage of very high order pure “hollow” LGp,l modes (p = 5 – 10, l = 7 – 28) was produced by this method for the first time. The region of stability of the resonator with an intra‐cavity aberrating lens was found to be enclosed between “focusing” and “imaging” configurations in the cavity, which the aberrating lens could provide simultaneously. The mechanism of LGp,l mode selection in such a cavity and possible applications of the proposed laser scheme are considered. (© 2010 by Astro Ltd., Published exclusively by WILEY‐VCH Verlag GmbH & Co. KGaA)