Abstract: A method of non-destructively inspecting a curved wall portion of a large and thick walled vessel for a defect by computed tomography is provided. A collimated source of radiation is placed adjacent one side of the wall portion and an array of detectors for the radiation is placed on the other side adjacent the source. The radiation from the source passing through the wall portion is then detected with the detectors over a limited angle, dependent upon the curvature of the wall of the vessel, to obtain a dataset. The source and array are then coordinately moved relative to the wall portion in steps and a further dataset is obtained at each step. The plurality of datasets obtained over the limited angle is then processed to produce a tomogram of the wall portion to determine the presence of a defect therein. In a preferred embodiment, the curved wall portion has a center of curvature so that the source and the array are positioned at each step along a respective arc curved about the center.