A method of and furnace for burning waste material. The furnace has a cenl chute for receiving the waste material, and a combustion chamber which is arranged below the chute and has a closed bottom. The transition between the central chute and the combustion chamber is designed as a constriction. The waste material is accumulated above the constriction, where it is dried and degasified up to the point of combustion by being heated up under the exclusion of air in the central chute. Heated up fresh air is supplied ahead of the constriction at below stoichiometric ratio to the heated up waste material and to the exhaust gases formed during the heating up of the waste material. The exhaust gases are withdrawn downwardly through the constriction, and further fresh air is supplied to the exhaust gases and to the degasified waste material for their common combustion at the constriction, so that essentially only ashes pass downwardly into the combustion chamber through the constriction. Fresh air supply lines discharge at the constriction and in the lower portion of the chute above the constriction. A portion of the combustible gases resulting during the degasification and the destructive distillation of the waste material are removed at the constriction. The flue gases formed in the combustion chamber are guided to a flue through discharge openings in the exhaust chamber of the combustion chamber. The exhaust chamber is designed in such a way that it surrounds the central chute. A device is provided in this chute for storing the waste material. Conduits, which extend into the chute from outside and are connectable to a suction device, discharge at the constriction.