Crystals with cylindrical symmetry, not existing in nature, are mimicked by the roll-up of single-crystalline and highly strained semiconductor bilayers. Exploiting this, the local structure of such individual rolled-up nanotubes is locally probed and quantified nondestructively by x-ray microbeam diffraction. A comparison to simulations, based on the minimization of the elastic energy, allows us to determine layer thicknesses and lattice parameter distributions within the strongly curved bilayers.