We describe a numerical model of the coupled gas‐phase hydrodynamics and chemical kinetics in a silicon chemical vapor deposition (CVD) reactor. The model, which includes a 20‐step elementary reaction mechanism for the thermal decomposition of silane, predicts gas‐phase temperature, velocity, and chemical species concentration profiles. It also predicts silicon deposition rates at the heated reactor wall as a function of susceptor temperature, carrier gas, pressure, and flow velocity. We find excellent agreement with experimental deposition rates, with no adjustment of parameters. The model indicates that gas‐phase chemical kinetic processes are important in describing silicon CVD.