The distribution functions are considered for the random sampling in space of a three‐dimensional acoustic mode. These functions are of interest when it is desired to estimate either the total acoustic energy present in the space, from a finite number of sample values, or the driving‐point impedance at an arbitrarily chosen point. Expressions are obtained for the probability density function (pdf) and cumulative function for a single mode excited in an ideal elastic fluid in a right circular cylindrical enclosure. Two kinds of axisymmetric mode are considered, those corresponding to the first zeros of the zero‐ and first‐order Bessel functions. The distribution functions obtained are compared with those for modes in a rectangular enclosure [R. V. Waterhouse, J. Acoust. Soc. Amer.47, 961–967 (1970)], and exhibit some novel and interesting features. For the cylindrical modes, the pdf's differ for each order of one type of mode, and in general have discontinuities, the number of which increases with the mode number. In both these respects the cylindrical modes differ from the rectangular modes.