The invention concerns a method for treading a tyre body comprising the following steps: the tyre body (2) being thus covered having been mounted on a rim (6, 6') and inflated, it consists in positioning on the running tread (3) an annular elastic mould (7) having an annular inner surface for moulding the running tread (3); providing between each tyre bead (21, 22) and each peripheral edge (71, 72) of the mould (7) an elastic rim flap (8, 9) which covers the outer surface of the tyre outer casing located between said tyre bead and said edge; setting the whole assembly (1, 7, 8, 9) in a pressurised and heated chamber.
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