Abstract: The determination of the numerical rank of a matrix by using computer and its application to control system analysis is discussed. It is shown by some typical examples that the traditional concept of rank and algorithm for its determination are not suitable for numerical computation. The concept of numerical rank and algorithm for its determination are then introduced. The singular value decomposition is employed in this algorithm. The numerical stability of the algorithm is analysed. Furthermore, the algorithm is applied to the determination of controllability and observability of control systems. As an example, the alignment of a Schuler platform is discussed.