The effect of the shape and dimensions of zinc oxide nanocrystals on the spontaneous luminescence decay times and the thresholds of stimulated luminescence in the ultraviolet spectral region is studied. It is shown that the columnar nanocrystals with hexagonal faceting exhibit the lowest threshold power of optical excitation for the diameters of the nanocavities are 100-200 nm, comparable to the absorption length for the excitation light. Different mechanisms of lasing are established for nanocrystals shaped as prisms and pyramids with a hexagonal base. Variations in the decay times and lasing thresholds can be attributed to different local densities of photon states in regularly shaped nanocrystals.