A model for overlapped operation between the control unit (CU) and processing elements (PEs) in an SIMD machine is presented. The major requirements and structure of the CU for overlapped operation in SIMD mode are described and overlapped operation is formally defined. To use the computing power of both the CU and the PEs most effectively to execute a single program, a balanced work load between the CU and PEs is required. It is assumed that certain computations (e.g., the manipulation of loop index variables, PE-common array index calculations) can be migrated from the PEs to the CU and vice versa.This research demonstrates how to increase the effectiveness of an SIMD machine by allowing overlapped operation between the CU and PEs. The best overlapping can be achieved ideally by assigning an equal amount of work to be executed concurrently on the CU and PEs, resulting in a 2N speedup for an N-PE system. The goal of this research is to develop a model of overlapped operation in SIMD mode so that the actual maximum possible performance of the SIMD machine can be attained. © 1991.