The applicability of the new DAP computer to problems involving lattices is assessed. As this computer uses a fixed number (4096) of parallel processing elements (PEs) this restricts the freedom of choice of sample shapes. It is shown, however, that there is usually no disadvantage in this restriction, and that in cases where a greater flexibility is needed, this can be achieved through user's software. The setting up of equitable lattices in three and four dimensions is detailed, using both skew and straight cyclic boundary conditions. The problems of lattices with a basis are considered, even those lattices which demand an odd number of elements. It would appear that there is no lattice in any dimension which cannot be implemented on the DAP, though sometimes the programming of logical masks is necessary. The efficient masking ability of the DAP lessens this disadvantage.