||In this thesis, I study the ultrasonic properties of three dimensional (3D) phononic crystals, consisting of 0.8 mm-diameter tungsten carbide beads immersed in water or in epoxy. The beads were close packed in a face-centered-cubic (fcc) crystal structure, with the triangular layers perpendicular to the body-diagonal direction. Phenomena associated with phononic band gaps (spectral gaps), ultrasound tunneling, anomalous dispersion and phonon focusing were investigated in some detail. Using pulsed ultrasonic techniques we measured not only the transmission coefficients but also the phase velocity and group velocity. As the phase information is important for studying the dynamics of wave propagation, a more complete picture of the wave dynamics was thus obtained. Large complete gaps were theoretically predicted for the tungsten carbide/water sample (0.98 MHz to 1.2 MHz) and the tungsten carbide/epoxy sample (1.5 MHz to 3.9 MHz). These predictions were supported by experiments. By studying the sample thickness dependence of the group velocity inside the gap frequencies, we demonstrated ultrasound tunneling through phononic crystals. The effect of absorption on ultrasound tunneling was examined. Anomalous dispersion phenomena in phononic crystals were studied using the tungsten carbide/water samples. A strong suppression of the group velocity, and large variations of the pulse dispersion (i.e., the derivative of the group velocity over frequency) were found at frequencies around the upper and lower edges of the L gap. At 1.6 MHz (inside the pass band), we also observed the phonon focusing phenomena. All experimental measurements carried out in this thesis are underpinned by theoretical calculations based on a multiple scattering approach. Comparisons between theory and experiments provide understanding of the results obtained, as well as point out further questions that arise fiom the discrepancies.