This master thesis focuses on the development of an numerical model to simulate the transport of dust particles eroded from land surface and convected by wind flow. The first part of this thesis is the literature review about existing methods to model the transport of dust particles. Analytical methods may produce some solution on given condition while numerical solution may extended to an even wider application with arbitrary boundary conditions appearing naturally. Based on these methods, the erosion mechanism is that once the friction velocity lager than the threshold friction velocity, particles are generated and entering the air becoming free particles which can be convected by wind flow. The second part is another core of this thesis, where we focus on the finite element methods to solve the mathematical model proposed for the dust transport. Special techniques have been introduced considering the convection dominated cases which will cause unstable solutions of the problem, while the shock capturing method are also used to eliminate the the local oscillations appearing in regions where solution has sharp gradient. In the last part we implement our model in FEMUSS, which is a multiphysics simulation software written in Fortran 2003. Specified cases are designed in order to verify the effectiveness of the code and model. Numerical tests show that our model works very well and gives more accurate solutions. The mechanism found in the experiments can be reproduced by our numerical solution. In order to take advantage of numerical methods, we also present a real application of our model trying to simulate the dust transport in a large wind tunnel, where we can see the concentration dynamics evolve with time.