Every new generation of scientific computers has opened up new areas of science for exploration through the use of more realistic numerical models or the ability to process ever larger amounts of data. Concomitantly, scientists, because of the success of past models and the wide range of physical phenomena left unexplored, have pressed computer designers to strive for the maximum performance that current technology will permit. This encompasses not only increased processor speed, but also substantial improvements in processor memory, I/O bandwidth, secondary storage and facilities to augment the scientist's ability both to program and to understand the results of a computation. Over the past decade, performance improvements for scientific calculations have come from algorithm development and a major change in the underlying architecture of the hardware, not from significantly faster circuitry. It appears that this trend will continue for another decade. A future architectural change for improved performance will most likely be multiple processors coupled together in some fashion. Because the demand for a significantly more powerful computer system comes from users with single large applications, it is essential that an application be efficiently partitionable over a set of processors; otherwise, a multiprocessor system will not be effective. This paper explores some of the constraints on multiple processor architecture posed by these large applications. In particular, the trade-offs between large numbers of slow processors and small numbers of fast processors is examined. Strategies for partitioning range from partitioning at the language statement level (in-the-small) and at the program module level (in-the-large). Some examples of partitioning in-the-large are given and a strategy for efficiently executing a partitioned program is explored.