Expressions for the neutron flux at the exit of a cylindrical duct of radius δ and length l (with λ = δ2/l2), have been found by the use of the albedo concept and by the method of single-collision sources in the duct wall, based on monoenergetic integral transport theory. In contrast with other methods of solution, the isotropic area source of radius δ at the duct entrance is not approximated by a point source, and the numerical evaluation of integrals does not impose restrictions on the values of λ. Calculation of the neutron flux at the duct exit is expedited by the use of the tables given, which are a function of the duct geometry and were generated from the numerical evaluation of the integrals that appear in the expressions for the flux. Comparison of the results as predicted by the formulas developed in this paper and those predicted by already existing formulas with the results of a stochastic neutron-transport code indicates that the formulas developed here are always in better agreement with the results of the code. For values of λ < 1, the formulas developed here differ by a maximum of ± 10%, while the existing formulas differ by a maximum of more than 100%.