This paper gives a new and very simple method of calculating Dancoff factors in regular arrays of cylindrical fuel rods. This method is readily applicable to canned fuel, and comparisons with Monte Carlo calculations show that its accuracy is adequate for practical purposes. The paper also gives an extension of the standard equivalence theorem which, unlike the theorem itself, is accurate enough for practical work. This extension enables the resonance integrals of regular arrays to be calculated from the Dancoff factor and from calculations of the resonance integral in homogeneous mixtures. These methods have been compared with the very accurate Monte Carlo calculations of Levine; the result is most satisfactory.