The influence of the shape and size of zinc oxide nanocrystals on the threshold and directionality of lasing in the UV spectral region is investigated. Columnar-shaped nanocrystals with hexagonal faceting must have a diameter of 100-200 nm to provide sufficient optical excitation power for nanoresonators; this is comparable with the absorption length of the exciting light. A mode structure of the laser emission directed preferentially along the axis of the hexagonal prisms is observed. Different lasing mechanisms are established for nanoprisms and nanopyramids with a hexagonal base. High homogeneity in shape and size of ZnO nanocrystals, and the dependence of these parameters on the conditions of gas transport synthesis are established by electron microscope methods.