Previous analysis of the problem of thermal escape from planetary atmospheres by kinetic theory techniques is extended. The two restrictions previously used of (a) plane layer approximation, and (b) constant gravitational field within a scale height, are removed in order to make the problem physically more meaningful. The distribution functions, chosen for the transition domain, are consistent with the continuum type of distribution expected to dominate at the lower boundary. At the same time a discontinuity (at the escape speed) is built into the distribution functions, to allow for a microscopic incorporation of the boundary conditions at the upper boundary where the transition zone merges with the free flow domain. A simplified collision term of the BGK type is used, and the constant collision term in the model is adjusted so as to yield the exact diffusive flow in the collision dominated regime, which is the expected driving mechanism for thermal escape. A two‐component solution yielding analytic results is obtained by only allowing a spatial variation of the respective densities. The full four‐component solution can be shown to be reducible to two coupled first‐order differential equations with variable coefficients, and an expansion method of solution has been established else‐where. The well‐known barometric decay constant found in elementary solutions is shown to be a partial solution present in both the two‐component and the four‐component approximations.