A simple and accurate analytic method for calculating pressure vessel neutron damage >1-MeV fluence has been derived. The method employs asymptotic expressions for the one-speed neutron transport Green's function, together with an effective removal cross section, to propagate the neutron source from the core out to the pressure vessel. The spatial integration over the core neutron source is performed using a multipole expansion of the transport Green's function. The analytic method reproduces detailed (DOT) numerical calculations in both (r,ϴ) and (r,z) geometries to within 5%, and similar accuracy is expected in three dimensions.