Software tools for the solution of partial dierential equations using parallel adaptive ยฎnite element methods have been developed. We describe the design and implementation of the parallel mesh structures within an adaptive framework. The most fundamental concept is that of a hierarchical partition model used to distribute ยฎnite element meshes and associated data on a parallel computer. The hierarchical model represents heterogeneous processor and network speeds, and may be used to represent processes in any parallel computing environment, including an SMP, a distributed-memory computer, a network of workstations, or some combination of these. Using this model to segment the computation into chunks which can ยฎt into cache memory provides a potential eciency gain from an increased cache hit rate, even in a single processor environment. The information about dierent processor speeds, memory sizes, and the corresponding interconnection network can be useful in a dynamic load balancing algorithm which seeks to achieve a good balance with minimal interprocessor communication penalties when a slow interconnection network is involved.