For the purpose of providing experimental data to assess neutron streaming calculations, neutron flux measurements were performed along the axes of the steel-walled annular ducts set up in a water shield of the pool-type reactor JRR-4. An annular duct simulated the air gap around the main coolant pipe. Another duct simulated the streaming path around the primary circulating pump of the integrated-type marine reactor. A 90-deg bend annular duct was also studied. In a set of measurements, the distance Z between the core center and the duct axis and the annular gap width δ were taken as parameters, that is, Z = 0, 80, and 160 cm and δ = 2.2, 4.7, and 10.1 cm. The reaction rates and the fluxes measured by the activation method are given in terms of absolute magnitude within an accuracy of ±30%. An empirical formula is derived based on those measured data, which describes the axial distribution of the neutron flux in the steel-walled annular duct in reactor shields. It is expressed by a simple function of the axial distance in units of the square root of the line-of-sight area, Sl. The accuracy of the formula is examined by taking into account the duct location with respect to the reactor core, the neutron energy, the steel wall thickness, and the media outside of the steel wall. The accuracy of the formula is, in general, <30% in the axial distance between and .