Phononic crystals are composite materials with periodic distribution of two or more media. One of the most distinctive characteristics of phononic crystals is that the elastic wave propagation is prohibited in certain frequency gaps. The difficulty of computing the band structure of the phononic crystals lies in capturing the complex geometry and jump conditions effectively on the interface between the scatterer and the matrix. The computation of Phononic crystals is actually an interface problem in mathematics. In this talk, I will present the FEM for the computation of 3D interface problems and its application in phononic crystals, the properties of various materials are also discussed.