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A distributed data structure is a data structure that can be manipulated by many parallel processes simultaneously. Distributed data structures are the natural complement to parallel program structures, where a parallel program (for our purposes) is one that is made up of many simultaneously active, communicating processes. Distributed data structures are impossible in most parallel programming languages, but they are supported in the parallel language Linda and they are central to Linda programming style. We outline Linda, then discuss some distributed data structures that have arisen in Linda programming experiments to date. Our intent is neither to discuss the design of the Linda system nor the performance of Linda programs, though we do comment on both topics; we are concerned instead with a few of the simpler and more basic techniques made possible by a language model that, we argue, is subtly but fundamentally different in its implications from most others.This material is based upon work supported by the National Science Foundation under Grant No. MCS-8303905. Jerry Leichter is supported by a Digital Equipment Corporation Graduate Engineering Education Program fellowship.