This paper establishes some significant links between two areas: (i) relational parallel database systems; and (ii) the design and analysis of parallel algorithms. The paper begins with a fundamental but very simple observation: implementing a JOIN operation in the context of relational parallel database systems is at least as expensive as implementing an arbitrary PRAM computation. Thus, the efficiency with which a given parallel computer can support a parallel relational database where JOINs are fairly frequent is strongly related to the efficiency with which that computer can support the PRAM as one of its programmer's models. The main technical contribution is an efficient parallel algorithm for the JOIN operation on a model where, in order to use the available bandwidth effectively, communication has to be performed in large blocks.