In order to explain the difference between measured and calculated gas permeability coefficinets P(P1,P1) for a polymeric membrane dominated by free molecular flow, the surface diffusion flow was taken into account. The equation for P(P1,P1) in the case where these two flows occur concurrently was derived on the basis of the following assumptions: (1) The transport of a gas through a fine tube is given by where n is the net flux of molecules at the position x, σ, the surface concentration of sorbed molecules on the tube wall, r, the radius of the tube, f0, Maxwell’s reflection coefficient associated with the free molecular flow, m, the mass of one gas molecule, a(p), the thickness of the absorved gas layer, and P and T, the pressure and temperature of the gas, respectively. (2) σ is represented by the BET equation as a function of P and T. The expression of P(P1,P2) for a porous membrane having a wide pore size distribution was derived by solving the above equation when the total gas flux is the sum of the fluxes through the individual pores. The calculated values of P(P1,P1) for a polycarbonate membrane having straight-through pores agreed with the experimental values.