First, the relationships between the amplification or the attenuation of solitary waves and the initial amplitude of solitary waves as well as the structure parameters of the media are determined by direct perturbation method. Second, the solitary wave propagation in a microstructured solid layer is solved numerically using a four-order difference scheme constructed by linearization technique, and also the interaction of the solitary waves with different amplitudes are simulated. As a result, it is demonstrated that the solitary waves, under proper conditions, could be amplified or attenuated, even the solitary waves can propagate steadily in the microstructured solid layer, and the interaction of solitary waves does not influence their propagation characteristics.