A formulation of a global mathematical two-dimensional model for Thermal Plasma Chemical Vapor Deposition (TPCVD) is reported. Both gas-phase and surface chemical kinetics as well as ordinary and thermal diffusion are incorporated. Flow is assumed to be steady, laminar and swirlless at this stage. The results include velocity, pressure, density, temperature and chemical species distributions in the reactor, and the heat flux and the film growth characteristics at the substrate. The model has been applied to a low pressure diamond TPCVD. Two basic cases have been investigated : (1) supersonic jet regime, and (2) high speed subsonic jet regime. The results for both cases are presented and compared. In both cases, the hydrocarbon species needed for the diamond formation are assumed to be premixed in the plasma jet. The main conclusions are : (1) The low pressure high speed jets are very narrow and slow down only at the substrate through a bow shock, (2) the faster the jet, the bigger the total deposited amount of diamond but also the higher the heat flux and diamond growth rate nonuniformities.???: (1) supersonic jet regime, and (2) high speed subsonic jet regime. The results for both cases are presented and compared. In both cases, the hydrocarbon species needed for the diamond formation are assumed to be premixed in the plasma jet. The main conclusions are : (1) The low pressure high speed jets are very narrow and slow down only at the substrate through a bow shock, (2) the faster the jet, the bigger the total deposited amount of diamond but also the higher the heat flux and diamond growth rate nonuniformities.???