The improved incinerator is a concentric elongated tubular array, with an outer closed tubular housing or shell, an annular tubular heat exchanger in the form of a bundle of spaced open ended tubes inside the housing and spaced inwardly therefrom to define an annular air passageway therebetween and front and rear spaces, and a tubular combustion chamber having an open front end and an open rear end. The front end thereof is necked down and in the form of a small diameter tubular inlet immediately downstream of the combustion zone in the combustion chamber. A fuel line, a fluidized waste material line and an ignition system pass through the inlet into the combustion zone, along with heated air to initiate and maintain the desired complete combustion of the waste material. The air is preheated by blowing it into the passageway and around and over the heat exchange tubes, before passing it into the combustion zone. The waste gases exit the housing through an exhaust stack at the front of the incinerator, which stack can be in heat exchange with the blower duct, in order to also heat the air and cool the exhaust gases. The incinerator operates, in accordance with the present method, with improved efficiency, requiring less fuel and producing fewer exhaust gases.