Constant pressure internal combustion engine having an elongated combustion chamber which in some embodiments is folded back upon itself and has a rough, twisting interior side wall, a fuel inlet for introducing fuel into the chamber, a compression chamber in communication with the combustion chamber, means for varying the volume of the compression chamber and combustion chamber to form a mixture of fuel and air that burns as it travels through the chamber and is further mixed by the rough, twisting side wall of the chamber, an expansion chamber in communication with the combustion chamber, and an output member in the expansion chamber which is driven by pressure produced by the burning mixture, with the means for varying the volume of the compression chamber and the output member in the expansion chamber being connected together for movement in concert such that the pressure remains substantially constant within the combustion chamber. A gas flow separator near the fuel inlet forms one or more smaller volumes within the combustion chamber where the fuel can mix and burn with only a portion of the air introduced into the chamber. Long, sharp protrusions extend inwardly from the wall of the combustion chamber and form hot spots which help to provide complete combustion of the fuel mixture throughout the combustion chamber, and these protrusions, together with flow turbulators within the chamber, promote complete mixing and, hence, combustion of the fuel and air.