Thermally induced plane stress in GaN layers of different thicknesses, grown by metalorganic vapour phase epitaxy on sapphire, is investigated. Thin layers, characterized by isolated grains, are found to be stress-free. With increasing layer thickness, however, grains start to coalesce and stress can build up when the samples are cooled down following growth. As soon as the coalescence process is completed and a compact film has been formed, a maximum stress level is reached which does not further increase for still thicker layers. Therefore, it is proposed that grain edges enable non-compact films to elastically relieve in-plane stress.