Grand canonical molecular dynamics techniques are used to study small molecular penetrant permeation through polymeric media. Penetrants are modeled as hard spheres and square-well spheres. The polymer is modeled as a collection of hard chains and square-well chains. Glassy polymers are modeled using stationary chains while rubbery polymers are modeled using mobile chains. Facilitated transport polymers are also modeled by varying the square-well depth for specific sites along polymer chains. Penetrant partitioning, mutual diffusivity, solubility, and permeability (taken to be a product of diffusivity and solubility) are calculated as a function of reservoir chemical potential, barrier mobility, and, for the facilitating polymer case, the strength of the penetrant/facilitating site attraction. Penetrant diffusivity, solubility, and hence permeability are greater in a mobile barrier than in a stationary barrier. Diffusivity decreases and solubility increases upon the addition of facilitating sites to the barrier or upon increasing the strength of the penetrant/facilitating site attraction. Permeability decreases in these cases, contradicting our expectations concerning the phenomenon of facilitated transport. Comparisons are made between the permeation results presented here and experimental facilitated transport systems, (C) 1997 American Institute of Physics.