Abstract: Elastic wave propagation in two-dimensional solid-solid ordered and weakly disordered phononic crystals is studied by using finite-difference time-domain method. Theoretical results show that obvious band gaps in the ordered crystal could be found, while in the weakly disordered ones the band gaps could partially vanish. Furthermore, with increase of disorder, band gaps are destructed badly and prominently in the high frequency regime while slightly in the low regime. Comparing the energy transmission dependent on time, we find that the coda wave phenomenon is prominent in the ordered crystal while weakened in the weakly disordered ones, and the physical properties are discussed.