The transmission of elastic waves in infinite/finite unidirectional phononic crystals is investigated by using the boundary element method (BEM). For the infinite periodic structure, we use BEM to formulate a Bloch's eigenvalue problem which has a nonlinear property caused by the Hankel functions in the fundamental solution. This nonlinear eigenvalue problem is solved by employing a contour integral method and band gaps are found in the dispersion curves. For the finite structure, a certain number of layers for cells are given to connect the input and output domains. The numerical simulation shows that the finite structure also presents a frequency banded nature which coincides with the band gaps of the infinite structure.