This paper presents a new parallel structured lookahead multidimensional sorting algorithm. Our algorithm can be based on any sequential sorting algorithm. The amount of parallelism can be controlled using several parameters such as the number of threads, word size, memory/processor communication overhead, and the dimension of the algorithm. The proposed technique is ideally suited for general purpose graphic processing units and shared-memory massively parallel processor systems. It ensures that data being processed exhibits temporal and spatial locality to maximize the utilization of processor cache. The algorithm achieves a speedup even when a single processor is used. A lookahead algorithm is also proposed to achieve even higher speedup. The performance of the proposed algorithm is verified numerically and experimentally. © 2013 IEEE.