We study mathematical models of wave process in shearing mixtures of solid deformable bodies. The models are non-linear, namely, a partial strain tensor of each the component is regarded as finite. We obtain governing equations of second approximation that allow us to analyze non-linear interaction between waves of different frequencies. We study some peculiarities due to propagation of non-linear stationary waves of deformation (periodic waves and solitary waves) in a mixture and derive dependencies related their general parameters (wave amplitude, wavelength, speed of wave, coefficient of nonlinear distortion of wave shapes). In the case of classical behavior of solitary waves, a wave with higher amplitude is of smaller width and propagates at higher speed. It is shown that anomalous behavior of solitary waves may take place such that a solitary wave with higher amplitude is of higher width and propagate at lower speed.