We present theoretical results for acoustic band structures for cubic arrays of spherical water balloons surrounded by a mercury host. Multiple, complete acoustic band gaps (i.e., stop bands) are found for the face‐centered cubic (fcc), body‐centered cubic (bcc), and simple‐cubic (sc) lattices. These stop bands are widest for a volume fraction of ∼24% and the corresponding gap/midgap ratios are about 0.83, 0.77, and 0.62, respectively, for fcc, bcc, and sc lattices. We stress that such a simple three‐dimensional (3D) inhomogeneous system of liquids exhibits the largest stop bands ever reported for 3D elastic as well as for dielectric composites. For mercury balloons surrounded by water the gaps obtained are surprisingly small. ©1996 American Institute of Physics.