An Orthogonal Access Multiprocessing system allows a multiplicity of processors to access distinct rows or columns of a rectangular array of data elements concurrently. The resulting tightly coupled system is feasible with current technology and has been suggested for VLSI as a "reduced mesh." In this paper we introduce the architecture and concentrate on its application to a number of basic vector and numerical computations. We prove that the machine exhibits the same performance as any other system with the same number of processors within a factor of 3. Matrix multiplication, LU decomposition, polynomial evaluation, and solutions to linear systems and partial differential equations all show a speedup of O(n) for an n-processor system. The flexibility in the choice of the number of PEs makes the architecture a strong competitor in the world of special-purpose parallel systems. © 1989.