This study is concerned with a process known as fumigation in the grain industry. During this process, fumigant is injected at the inlet of storage and is expected to distribute throughout the stored grain to kill the insects in it. The present research focuses on the study of the fumigant (phosphine) flow distribution based on mathematical modelling and numerical simulation through available Computational Fluid Dynamic (CFD) software. In particular, the mathematical modelling is translated into the CFD and simulation is ran to determine areas where insects might find refuge. Hence provide information for conducting more effective fumigation. Numerical simulation using CFD software, for example, FLUENT, is widely known as cost and time effective. However, the numerical simulation needs to be verified before conducting such studies. For a simple case, the analytical solution exists. Therefore, the analytic solution for a simple case, can be used for verification and serve as a basis for adopting a CFD software, FLUENT for an extended geometry and boundary conditions. The numerical results are found to agree well with the analytical results. Overall, the fumigant gas flows towards the outlet regardless of the position of the outlet.