The problem of free molecule flow over concave surfaces is investigated, and general equations formulated for the lift, drag, and heat transfer characteristics of such surfaces. The effect of multiple reflections is taken into account by use of the Clausing integral equation to determine the redistribution of molecular flux over the surface. It is assumed that emission of molecules from the surface is purely diffuse, and that the reflected molecules are perfectly accommodated to the surface conditions. The equations obtained are solved for the cases of (i) an infinitely long circular cylindrical arc and (ii) a section of a spherical surface, at hyperthermal velocities. It is found that under the above conditions the local heat transfer characteristics are the same as those of the corresponding convex surface, the total heat transfer being independent of the geometry of the surface. As drag devices, the concave surfaces examined prove only slightly more effective than a flat plate at similar incidence, and as a generator of lift the cylindrically cambered plate is significantly inferior to the flat plate at similar incidence.