An analysis is presented for calculating the depletion characteristics (poison effective cross section, self-shielding, and spatial-flux distribution) of a cylindrical pin containing one isotope or a mixture of burnable poison isotopes. The analysis takes into consideration the anisotropy of incident neutrons. The resulting equations are programmed on a digital computer, and the results are in good agreement with the transport-theory calculations of the depletion. One of the particular merits of the presented analysis is the high degree of accuracy achieved and the shorter computation time required in comparison to similar transport-theory methods. To illustrate the method, sample calculations are performed for a cylindrical fuel pin containing 5% (wt%) gadolinium in a typical Boiling Water Reactor core lattice.