Experimental data and a supporting model are presented for the formation of voids in InN nanorods grown by selective area hydride vapor phase epitaxy (HVPE) on patterned GaN/c-Al2O3 templates. It is shown that these voids shape, due to a high lattice mismatch between InN and GaN materials, starts from the base and extends up to a half of the total length of the nanorods. When the effect of the mismatch between substrate and nanorods becomes weaker, the hollow nanotubes close up at the top and further growth proceeds in the standard nanowire geometry without voids. This effect is observed within a wide range of growth conditions during the InN synthesis and must be taken into account for controlling the final structure of InN nanorods for different device applications.