Sublimation seeded growth of bulk AlN single crystals in a resistance-heated furnace has been studied experimentally and theoretically. The growth temperature, the temperature drop between the AlN powder source and single-crystal seed, and the ambient nitrogen pressure are varied to find the optimal growth conditions. Ambiguous effect of the process parameters on the crystal growth rate is revealed; it is found, in particular, that the growth sharply slows down and even fails at a higher temperature and a lower source-seed temperature drop. Simulation of the process suggests that the effect is associated with certain evaporation of the seed under unfavorable growth conditions. The optimal growth conditions providing a stable growth of single-crystal AlN boules of about 10 mm diameter and 10 mm long at a rate of 0.3-0.5 mm/hr are found. The crystals grown at a near-atmospheric pressure have pronounced hexagonal facet shape, decrease of the pressure favors growth of more rounded crystals with a distinct stepwise surface and few growth centers.