We have attempted to simulate dispersion phenomena of aerosol bolus in a straight tube under the developing cyclic flow condition using finite element method. The computational scheme was first validated by solving pure diffusion equations and subsequently by comparing the computational results with analytical solutions. In simulating cyclic flow conditions, both symmetric and asymmetric velocity profiles were used between the forward and reverse flow. The diffusion coefficient of particles (dp = 1 µm) was assumed to be enhanced by flow turbulence generated during the decelerating phase of the cyclic flow. It was found that the axial dispersion is enhanced by radial diffusion during stretching and contraction of the aerosol bolus. The dispersion profile along the axial direction showed a good agreement with experimental data obtained under similar conditions. The results suggest that the flow turbulence generated during the decelerating phase and the velocity profiles in the forward and reverse flows may play a crucial role in determining aerosol dispersion in cyclic tube flow.