The inner mitochondrial membrane has been shown to have a novel structure that contains tubular components whose radii are of the order of 10 nm as well as comparatively flat regions. The structural organization of mitochondria is important for understanding their functionality. We present a model that can account, thermodynamically, for the observed size of the tubules. The model contains two lipid constituents with different shapes. They are allowed to distribute in such a way that the composition differs on the two sides of the tubular membrane. Our calculations make two predictions: (1) there is a pressure difference of 0.2 atmospheres across the inner membrane as a necessary consequence of the experimentally observed tubule radius of 10 nm, and (2) migration of differently shaped lipids causes concentration variations of the order of 7% between the two sides of the tubular membrane.