Rapid growth of the mobile communication market has triggered extensive research on the bulk as well as surface acoustic wave devices in the last decade. Quite a few important results on the modeling and simulation of Film Bulk Acoustic Resonator (FBAR) and Layered SAW devices were reported recently. The other recent advance of acoustic waves in solids is the so-called phononic crystals or phononic band-gap materials. Analogous to the band-gap of light in photonic crystals, acoustic waves in periodic elastic structures also exhibit band-gap. Important applications of phononic band gap materials can potentially be found with creating a vibration free environment in microstructures, and design of