Data partitioning and declustering have been extensively used in the past to parallelize I/O for range queries. Numerous declustering and disk allocation techniques have been proposed in the literature. However, most of these techniques were primarily designed for two-dimensional data and for balanced partitioning of the data space. As databases increasingly integrate multimedia information in the form of image, video, and audio data, it is necessary to extend the declustering techniques for multidimensional data. In this paper, we first establish that traditional declustering techniques do not scale for high-dimensional data. We then propose several new partitioning schemes based on concentric hyperspaces. We then develop disk allocation methods for each of the proposed schemes. We conclude with an evaluation of range queries based on these schemes and show that partitioning based on concentric hyperspaces has a significant advantage over balanced partitioning approach for parallel I/O.