Scalable parallel processing has been proposed as the technology scientists and engineers can use today to solve the problems of tomorrow. Many computational Grand Challenge problems require between two and three orders of magnitude than can be provided with the scalable parallel hardware of the early nineteen-nineties. While hardware continues to become more scalable and cheaper, software is not advancing at the same pace and remains a very expensive part of systems development. A great deal of emphasis on software technology to support scalable parallel processing is placed on von Neumann languages. One of two approaches is common: (a) augment the von Neumann language with explicit parallel constructs or (b) write super-optimizing compilers to “find” the parallelism in a von Neumann program. These two approaches appear to be useful at some level; however, this paper argues that software constructed using these approaches is not likely to scale very well, because an appropriate level of abstraction is not being used to solve the problem. We propose a simple layered architecture for doing parallel processing. The outer layer is the composition layer. This layer is used from a von Neumann language to encode algorithms using standard building blocks (objects). The middle layer uses objects. These objects exhibit high potential for parallelism. In our application, we focus on multidimensional arrays. At the lowest level, Itinerant Actors is used. Itinerant Actors is an object model developed by Christopher and Thiruvathukal at IIT to support asynchronous message-passing between active objects with a number of other useful ideas.