The invention relates to a method for chemical-looping combustion of a solid hydrocarbon-containing feedstock, wherein the ashes and fines are removed at the outlet of reactive oxidation zone R1 by sending transported phase (5) coming from reactive zone R1, comprising gas and solid, to a gas-solid separation zone S2, then by sending solid stream (7) coming from gas-solid separation zone S2 to a dense phase elutriation separation zone S3 fluidized by a non-reducing gas (8) allowing the fines and the fly ashes to be separated from the oxygen-carrying material particles. Optionally, deeper separation is carried out in a dedusting zone S5 arranged downstream from dense phase elutriation separation zone S3. The invention also relates to a chemical-looping combustion plant allowing the method according to the invention to be implemented.