The structure of anodized nanoporous alumina is described as a closely-packed hexagonal arrangement of monodispersed nanopores, of which size and interval can be controlled by changing the anodization conditions. Nanoporous alumina thin films with highly ordered hexagonal arrangement of various porosities represent a rather complicate system for elastic wave propagation. The periodic structure, the extremely high acoustic impedance contrast (alumina vs. air) and the possible existence of different polymorphs all can significantly affect the transportation of elastic energy, e.g. the generation of the so-called phononic bandgaps and the strong localization of elastic waves. Investigation of phonon propagation in such nanoporous alumina films is of both significant fundamental and applied importance. In addition, the mechanical anisotropy (in-plane vs. out-of-plane) associated with such two dimensional structures remains unexplored. Here we present preliminary results on elastic waves in these nanoporous alumina films studied by Brillouin light scattering (BLS).