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The stripe structures of stiffness matrices resulting from irregular domains covered by regular grids; are analysed. It is proved that the non-zero elements in these matrices may be covered by very few stripes, and that these stripes may be non-overlapping, if the nodes of the grids are numbered appropriately. The exact number of stripes, which is independent of the size of the problem, is derived for different types of grids, and different numbering schemes. The stripe structure of some irregular grids are also examined. Keywords: Parallel processing; partial differential equations.