The direct simulation Monte Carlo method is used to study neutral species transport in cylindrical, high plasma-density systems. This technique is well suited for the transition flow regime in which these reactors operate. The ground state neutral density is depleted in the volume of the chamber due to ionization and is enhanced at bounding walls due to ion-electron surface recombination. In addition, electron-neutral and ion-neutral collisions heat the neutrals resulting in further neutral density depletion. The influence of chamber geometry and fractional degree of ionization on neutral density profiles is explored for an electron cyclotron resonance system. Results for an extended source/downstream chamber and for a compact source chamber are compared.