The three-dimensional (3D) correction of glenoid erosion is critical to the long-term success of total shoulder replacement (TSR). In order to characterise the 3D morphology of eroded glenoid surfaces, we looked for a set of morphological parameters useful for TSR planning. We defined a scapular coordinates system based on non-eroded bony landmarks. The maximum glenoid version was measured and specified in 3D by its orientation angle. Medialisation was considered relative to the spino-glenoid notch. We analysed regular CT scans of 19 normal (N) and 86 osteoarthritic (OA) scapulae. When the maximum version of OA shoulders was higher than 10, the orientation was not only posterior, but extended in postero-superior (35%), postero-inferior (6%) and anterior sectors (4%). The medialisation of the glenoid was higher in OA than normal shoulders. The orientation angle of maximum version appeared as a critical parameter to specify the glenoid shape in 3D. It will be very useful in planning the best position for the glenoid in TSR.