Abstract: We establish a 2D diffusion mathematic model considering transverse diffusion and feature of channeling reservoir.With Laplace transform an analytical model is solved.A solution with small slug is found.With general-purpose finite element software in a geometrical model numerical solution is solved.2D concentration profile is ploted.It is shown that larger Peclet number leads to higher peak concentration and later break through time.With combination of analytic solution and numerical solution,it is helpful in understanding the essential of mass transfer diffusion.