In the theory of thermal radiation the radiant interchange between diffusely emitting surfaces is described by the use of angle factors. In this study the angle factors for the radiation transfer between the surface elements of two concentric cylinders are calculated analytically. This is achieved by replacing one surface integration in the equation for the angle factor by an integration over the direction of the radiation emitted from that surface. One result of the study is that analytical angle factors are given for geometrical transitions for which apparently no information is available in the literature. Furthermore, simplified expressions for the known angle factors are derived and tabulated in a consistent notation facilitating their use in practical applications. The angle factors thus obtained can be easily evaluated numerically and used in heat transfer or neutral particle streaming calculations in r-z geometry.