The transmission of gamma rays through a straight cylindrical duct from an infinite plane source has been studied both theoretically and experimentally. The distribution of the resulting dose in the vicinity of the duct was calculated by the ray-analysis method, with the exception that the dose arising from radiation scattered within the duct was calculated by a semi-analytical Monte Carlo method. These results, together with those from experiments, lead to useful conclusions. Data applicable to the design of small ducts through shields have been developed for a range of various geometric parameters.