An engine with mesh anchored combustion with a pressure regulating auxiliary chamber for providing controlled internal combustion at essentially a constant pressure. The engine comprises a main cylinder and piston with an auxiliary chamber and piston integral therewith. The auxiliary chamber is adjacent to the main cylinder head, connected thereto through a relatively narrow throat. A mesh is positioned in the throat at the boundary of the main cylinder and the auxiliary chamber. Accordingly, when the main piston compresses a charge in the main cylinder during its compression stroke, the charge is pushed through the mesh into the auxiliary chamber. The auxiliary chamber piston pushes the charge in the reverse direction back through the mesh into the main cylinder. As the charge passes through the mesh back into the main chamber, its combustion forces the main piston back down toward bottom dead center.