The band structure and the displacement field of elastic waves in periodic/disordered layered composite structures of finite width are investigated by a simple mass-spring model. In the case of comparable stiffness, the density contrast plays a dominant role for the center layer disorder to obtain localized wave modes within the band gap. On the other hand, in the case of comparable density contrast, the number and the position of the localized modes can be adjusted by changing the stiffness of the center layer. Compared to the soft and nearly cracked disorders situated between two layers with a lower density, the band structure and the displacement are quite different from the case between two layers with a higher density.

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