Abstract: The propagation characteristics of stress waves in the solids with variable section was dissection. Based on the one-dimensional longitudinal wave motion theory and the harmonic analysis, the rules of the dispersion of the wave shape and the change of the wave amplitude which are due to the variation of the section are obtained, the wave evolution factor combined with the variable section is deduced, and the two-dimensional effect, such as the geometry dispersion due to the variation of the section, is discussed. The rules how the geometry parameters and section shape functions effect the evolution of stress waves in the solids are also calculated and discussed.