A parallel computer of a MIMD array type suitable for high speed computations in engineering and science, comprising a master unit, N submaster units and a two dimensional array of N.sup.2 arithmetic units having own processors and private memories respectively, and further N common memories each of which is used for transferring some data between a submaster and a corresponding set of N arithmetic units, and finally a three dimensional array of buffer memories with a capacity being composed of N grand boards each (alternatively the k-th grand board) of which has N.sup.2 memory units and is provided for transferring some data between every pair of an arithmetic unit being on a (the k-th) row of the arithmetic unit array and another unit being on the corresponding (the k-th) column.