Abstract We propose a stable finite element method for approximating the flow of a chemically reacting gas mixture in an MOCVD (metal‐organic chemical vapor deposition) reactor. The flow is governed by the full compressible Navier‐Stokes equations extended by transport equations for the chemical species, the energy equations and the equation of state, together with boundary conditions providing information on the reactor geometry and experimental conditions. The equations form a semilinear system with a constraint for which the corresponding pressure term is not the Lagrangian multiplier. An application of our method to a real world model of growth of GaAs shows the consistency with experimental data. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005