The transverse impact of variable cross-section flexible beam has been investigated. According to the effect of the section property and the impact force，the flexible beam was divided into several elements. First of all，the differential equation of the collision system, the boundary conditions and the continuity conditions were transformed with laplace transformation. The solution of the stress wave in frequency domain was educed. And then，numerical inverse method was demonstrated by using the inversion of laplace transformation with Crump. Finally，the dynamic response in time domain was obtained. The diagrams of impact force，displacement, shear stress and normal stress were gained by applying a numerical example. The effect of variable cross-section for dynamics response was displayed and this proposed method was verified by comparing its results with those by using the finite element method. This method can be promoted to solve the multi-point transverse impacting problem of structures.