Constant pressure internal combustion engine having compression and expansion chambers of variable volume, an elongated combustion chamber of substantially constant volume between the compression and expansion chambers, and a fuel inlet for introducing fuel into the combustion chamber where it mixes with compressed air from the compression chamber to form a mixture of fuel and air that burns as it travels through the combustion chamber. In some embodiments, the combustion chamber is folded back upon itself and has a rough, twisting interior side wall, with long, sharp protrusions extending inwardly therefrom and forming hot spots which help to provide complete combustion of the fuel mixture throughout the combustion chamber. These protrusions, together with flow turbulators within the chamber, promote complete mixing and, hence, combustion of the fuel and air in the combustion chamber.