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This paper presents a modular algorithm which is suitable for computing a large class of multidimensional transforms in a general purpose parallel environment without interprocessor communication. Since it is based on matrix-vector multiplication, it does not impose restrictions on the size of the input data as many existing algorithms do. The method is fully general since it does not depend on the specific nature of the transform kernel and, therefore, it may be used for a wide variety of transforms. Moreover, since some one-dimensional Fast Fourier Transform algorithms map the input sequence onto two or more dimensions, the new method also may be employed to efficiently compute the 1D FFT in parallel. In addition, the proposed algorithm is exploited to derive a fully systolic VLSI architecture performing multidimensional transforms, which does not need the transposer required by classical architectures.