The present disclosure relates to a tool for supporting and locking a rim or tired wheel in position on a tire mounting-demounting machine for automobile wheels equipped with support table (2) with an axial hole or opening (2a), the tool comprising grip-release device (3) for a tired wheel (TW) or a rim (W) to be handled, and locking means for locking the grip-release device (3) to the support table (2) and/or for locking the rim (W) or tired wheel (TW) against components of the grip-release device (3).