A process for demounting a tire P, and a tread-bearing support S internal thereto, from an integral mounting rim J, which comprises first and second rim seats, the two rim seats being inclined towards the outside and extended axially to the outside by projections of low height. The process includes the steps of inserting, into a lubricated gap between the toe of the first bead Bo and the corresponding rim seat, a demounting insert I in the form of a portion of a circular ring of triangular meridian section of small dimensions, and then ejecting the first bead Bo from the rim J before or simultaneously with the ejection of the tire/support assembly.