We consider steady-state flow of real gases through bounded, randomly heterogeneous porous media. Such flowis described by a nonlinear partial differential equation with the random coefficient (medium s permeability) and source terms subject to randomly prescribed boundary conditions. Prior to applying stochastic analysis, the problem is linearized by means of the Kirchhoff transformation which allows us to obtain the exact expressions for an effective (upscaled) gas permeability. In particular, for one-, two-, and three-dimensional mean uniform flows in infinite, statistically homogeneous and isotropic domains the resulting effective permeability is given by harmonic, geometric, and arithmetic averages, respectively. The influence of statistical anisotropy of the random permeability field and domain s boundaries on the effective gas permeability is also investigated.