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This paper aims at studying the band gap phenomena of three-dimensional phononic crystals using the finite difference time domain (FDTD) method and a PC cluster system. In the paper, Bloch's theorem is applied to the wave equation and to the boundary conditions of the periodic structure. We calculate the variations of displacements and take discrete Fourier transform to acquire the resonances of the structures. Then, the dispersion relations of the bulk acoustic wave can be obtained and the band gaps are predicted accordingly. On the other hand, because of larger data calculation in three-dimensional phononic crystals, we introduce the PC cluster system and parallel FDTD programs written with respect to the architecture of a PC cluster system. Finally, we discuss the numerical calculation of two-dimensional and three-dimensional phononic crystals consisting of steel/epoxy and draw conclusions regarding the band gap phenomena between these phononic crystals.