Abstract: In a method of incinerating waste material in a parallel flow process wherein hot exhaust gases are conducted above a combustion chamber grate in the same direction as the material is moved on the grate, different temperatures zones are maintained to which air is admitted from the bottom through the grate such that a temperature of less than 900.degree. C. is maintained in a first zone which is a drying zone, a temperature of about 1000.degree. C. is maintained in a second zone which is an evaporization and vaporizing zone, a temperature of about 900.degree. C. is maintained to in a third zone, which is the final combustion zone and a temperature less than 900.degree. C. is maintained in a fourth zone which is a sintering zone. Additional air is supplied to the combustion zones 1 through the side walls of the combustion chamber.