We extended our earlier models for direct resonance energy transfer (DET) on systems of planar and spherical symmetry to cylindrical domains. The model we now develop applies to systems with restricted geometries and arbitrary distribution functions of donors and acceptors with cylindrical symmetry. The method enables one to evaluate the donor decay function from the donor and acceptor concentration profiles without requiring prior calculation of the donor-acceptor pair distribution, even when the donor translational invariance requirements of the Klafter-Blumen methodology are not satisfied. The formalism was applied to simple systems in which the donors may or may not occupy equivalent positions. For the first case, our results are compared to and are shown to agree with previously known models. For the second case, we have obtained new expressions for the donor decay function. Finally, we discuss whether certain specific geometries could be distinguished from one another by single-photon-timing fluorescence measurements on dye-labeled samples.