A model containing q PDE's is used to study long-range transport of air pollution over Europe. Four physical processes, advection (transport due to the wind), diffusion, deposition and chemical reactions (including here also the emission sources) are united in the model. By splitting procedure (according to the physical processes involved) and by a space discretization the system of PDE's is transformed into four huge systems of ODE's. On a 32 × 32 × 9 space grid each system of ODE's contains 267264 equations in the case where q = 29. Even when the model is considered as a 2-D model (on a 32 × 32 space gride), the number of equations is still very large, 29696 in each system of ODE's. The results obtained in the preparation of kernel subroutines for the 2-D model are discussed. It is shown that a 2-D model, which is numerically tractable on vector processors, can be developed by a careful choice of the algorithms and by vectorizing the most time-consuming parts of the code.It should be emphasized, although this is probably not a great surprise, that the most time-consuming operations in the model are fairly general and well-known operations: matrix-vector products and FFT's. New and efficient band matrix-vector multipliers, as well as results obtained with multiple FFT's from the NAG Library, are discussed.