The periodic vibration of a free reed subject to a steady pressure gradient (bellows pressure) is examined from a fluid dynamics approach. In this analytic study, the self-excited forcing function is modeled from the static and dynamic pressures acting on the vibrating tongue surface. A first formulation includes standard mounting of the reed over a cavity, with a hole that accommodates a mean air flow to the outside. A second formulation includes in addition a resonant air geometry that could include non-standard operation, such as pitch bending.