We study theoretically the pressure and gas flow fields produced by a deflagration wave as it passes down a cylindrical detonator delay element filled with a porous pyrotechnic. We model the flame front as a planar source of heat and gas which travels down the element with constant speed, thus eliminating the detailed chemistry of the reaction. It is shown that there are two key small dimensionless parameters beta (the aspect ratio) and delta (a measure of the permeability of the porous pyrotechnic). The pressure field and mass flow circulation is studied for punctured and sealed elements.