Abstract The problem of calculating radiation streaming in a duct is discussed. Methods used for such calculations are summarized. A technique is presented which combines diffusion theory in material regions with line-of-sight kernels in a void within the same code. The finite-element diffusion code FENDER has been modified so that a void region may be specified; and the diffusion equation is solved for the system excluding the void. Emergent currents at the void boundary are calculated. These are coupled with line-of-sight kernels to produce incident currents on the void boundary which are used as additional source for a further diffusion theory calculation in the material regions. An iterative procedure is carried out until the solution for the whole system converges. Results are presented of a test case which involves the streaming of thermal neutrons along a three-legged steel-lined duct in a graphite medium.