We consider a medium of non‐negligible optical depth in which high energy line photons are Compton scattered. For the calculation of the angle and energy dependent specific intensities we first cast the correlations between the angles and energies of the incoming and the outgoing photons (as determined by the Compton conditions) into the form of a redistribution function, which is weighted by the Klein‐Nishina cross‐section in order to account for the energy dependence. We then discretized the angle × energy space so that the radiative transfer equation transforms from an intergro‐differential equation into a system of ordinary differential equations subject to boundary conditions on both sides. This system is subsequently solved in a numerically stable way without any further approximation by means of the discrete‐ordinate‐matrix‐exponential (‘‘Dome’’) method so that all emergent intensities and the energy converted into heat are obtained.Since the redistribution function is very complex and involves singular hyperplanes, our algorithm requires a relatively large memory space whereas the CPU times are rather modest, e.g. for 16 angles and 25 energies in both the input and the output channel, 30 Mby of memory and 30 sec of CPU time are needed on an IBM 3090 VF independent of the actual optical depth.First results for a plane‐parallel medium, which consists of cold electrons and which is irradiated from one side by &ggr; line photons, are presented and the accuracies of the derived radiation fields are discussed.