It is well known that the steady‐state flow of a gas past a solid obstacle immersed in a space filled with isotropic scattering centers can be represented by an integral equation for the collision density distribution. Asymptotic expansions are developed for the gas flux in the form of a power series in the mean free path&lgr;, the leading term representing the continuum diffusion limit. The method replaces the original integral equation with a series of problems, each requiring the solution of a Poisson equation with inhomogeneous terms of increasing complexity. The case of a spherical obstacle of radiusRis treated explicitly; two iterations give the reduction in the flux correct to order&lgr;2. It is found that at moderate&lgr;the sphere acts as though its radius had increased by3&lgr;/16R.