Pneumatic vehicle tire, in particular a run-flat tire, having a carcass, a tread, and two tire beads, having a respective bead core, which are provided for fixing the tire in an associated wheel rim by the fact that the beads overlap with the associated wheel rim. According to the invention, to avoid relative motion between the tire bead and the wheel rim when the tire is subjected to impact load, the bead is designed in such a way in the nonloaded state mounted on the wheel rim the bead does not overlap with the wheel rim in the contact region of the wheel rim flange above the bead core.