In this paper, some boundednesses and inadequacies of the traditional fluctuation theory were pointed out. Then the establishment and derivation process of a modified elastic wave theory was given. The conversion process of wave equation from tensor state to column coordinate system was completed and the wave equation under column coordinate system was obtained. The relationship between the fluctuation variables and the load and velocity on the loading surface was established, revealing the influence of the boundary condition on the fluctuation variables when the stress wave reflection occurred on the free surface. By using Matlab programming, propagation process of the stress wave was calculated in the hollow cylindrical structure with an infinite length in the z direction of the geometric model and so was its reflection when encountering with the boundary. The calculation results showed the propagation process of stress wave in the structure with time, during which the stress wave would produce two waves on the loading surface, namely the volume wave and the deformation wave, and four waves would be reflected when encountering the boundary. At the same time, the volume wave and the first part of the deformation wave would be combined to form a composite pulse moving at the same wave speed.