A method and apparatus for demounting a pneumatic vehicle tire, the beads of which, in the mounted state, are disposed on the radially inner periphery of a wheel rim having a deep mounting bed and, laterally outwardly therefrom, rim flanges which extend essentially radially inwardly. First, a portion of a given tire bead is forced into the deep mounting bed, and subsequently the oppositely located portion of the same tire bead is lifted over the rim flange.