We report on the experimental and theoretical investigation two kinds of acoustic waves in two dimensional phononic crystal: bulk acoustic waves and surface acoustic waves. For bulk acoustic waves, the work focuses on the experimental observation of full acoustic band gaps in a two-dimensional lattice of steel cylinders immersed in water as well as deaf bands that cause strong attenuation in the transmission for honeycomb and triangular lattices. For surface acoustic waves, complete acoustic band gaps found experimentally in a two-dimensional square-lattice piezoelectric phononic crystal etched in lithium niobate will be presented. Propagation in the phononic crystal is studied by direct generation and detection of surface waves using interdigital transducers. The complete band gap extends from 203 to 226 MHz, in good agreement with theoretical predictions. Near the upper edge of the complete band gap, it is observed that radiation to the bulk of the substrate dominates. This observation is explained by introducing the concept of sound line.