The acoustic band gap structures for rectangular arrays system made of elliptical water cylinders surrounded by a mercury host were investigated by plane wave expansion method. Multiple, complete acoustic band gaps were found for different elliptical cylinder radii and rotating angles. When lattice constants a1=4cm，a2=3.2 and filling fraction F=0.35, there is only one complete band gap and the corresponding width is 0.453 for rotating angle being 0, but there are three complete band gaps and the corresponding widths are 0.458, 0.023 and 0.062 respectively for rotating angle being π/4. It can be concluded that, in such a simple twodimensional inhomogeneous system of liquids, the acoustic band gap structures are affected by the filling fraction, the shape of elliptical cross section,and the rotating angle