An analytical solution for the transient two-dimensional atmospheric pollutant dispersion problem is presented. The approach used in this problem utilizes the double GITT (Generalized Integral Transform Technique), the Laplace Transform and the matrix diagonalization. Furthermore, mathematical filters are used due to the existence of non-homogeneous boundary conditions. The results we obtained are compared with experimental data for short range downwind dispersion utilizing two well-known experimental dispersion datasets (Copenhagen and Prairie Grass). It is shown that the present analytical approach give good results for downwind concentration except for receptors very close to the release points were any Eulerian approach based on K-closure is known to fail.