Sound propagation through rows of periodically arranged circular cylinders, immersed in a fluid and filled with another fluid, is studied. Each row of the bundle acts like an acoustic diffraction grating - the scattering behaviour is described by grating theory incorporating the motion of individual cylinders. Emphasis is placed on cases in which the scattered field contains a superposition of propagating plane waves travelling in different directions. Tube bundles with either a finite, or an infinite, number of rows are considered. For the finite bundles, various patterns of row spacings are examined. When dealing with an infinite number of rows, they are assumed to be equally spaced and defined to be a periodic layered medium. Results for the transmission and reflection matrices of these bundles are presented for the frequency range (0-200 \mathrm{kHz}). The formation of passing and stopping bands for a finite number of rows has been observed; the passing bands are generally wider for bundles with equally spaced rows than for bundles with unequal row spacing. The transmission spectra (per tube row) for a finite number (20) of equally spaced rows matches closely the Bloch transmission spectra for the analogous periodic layered medium. Calculations have also been performed to highlight various properties that have particular practical significance.