Simple longitudinal waves in an inhomogeneous solid which has the microstructure in the form of granulae in matrix (in a typical granular composite) are studied. Three microstructural models for describing of a granular composite are used: model of the effective nonlinear elastic medium; model of the linear elastic two-phase mixture. For all models the same simple wave is investigated. It is described analyticall by Tshebyshov-Hermite function of null index. That is a solitary wave with the classic bell-shaped profile. In the frame of first model the distortion of a bell-shaped wave owing to material nonlinearity is studied. Computer plots of a new wave which distorts the basic profile are built.
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