The models of elastic waves in one-dimensional compound materials， including one-dimensional periodical phononic crystals， abnormal Fibonacci qusi-periodical phononic crystals， generalized Fibonacci qusi-periodical phononic crystals and absolutely disordered compound materials， are proposed in this paper. The transmission coefficients of elastic waves through the above systems are numerically calculated using the mode matched theory method. The results shows that larger band gap can be obtained， and much more localized modes are present in the band gap of a given quasi-periodical structure phononic crystals than in the periodical phononic crystals. The effect of quasi-periodical structure is the same as that of the prcsence of defects in periodical phononic crystals. The study of the localized states of elastic waves/acoustic waves in compound materials is useful to the fabrications of the elastic/acoustic wave filters or wave-guides.