This paper studies the vibration characteristics of the phononic crystal beam on elastic foundations, based on the Euler beam theory and the Winkler foundation model. The finite element method is used to obtain the band structures of phononic crystal Euler beams. The results reveal the influence of the foundation constraint on the bending vibration band gaps in the phononic crystal Euler beam. The computational results of the band structures of the phononic crystal Euler beam without foundation are compared with those on the elastic foundation. The significantly different band gaps of the model are shown. The influences of different component ratioes of the phononic crystal Euler beam model are also studied, as well as the frequency ranges of the vibration band gaps.