Astronomical data sets are beginning to live up to their name, in both their sizes and the complexity of the analysis required. Here we discuss two astronomical data analysis problems which we have begun to implement on a hypercube concurrent processor environment: The intensive image processing required in an optical interferometry project, and the large scale power spectral analysis required by a search for millisecond-period radio pulsars. In both cases the analysis proceeds largely in the Fourier domain, and we find that the problems are readily adapted to a concurrent environment. In the following report, we outline briefly the astronomical background for each problem, then discuss the general computational requirements, and finally present possible hypercube algorithms and results achieved to date.