A systematic procedure is presented for calculating the least stable condition in a reactor system that can occur within the uncertainty range on system parameters. This uncertainty range is due to the impossibility of perfectly predicting design parameters and the effect of aging of the system on these parameters. The method uses the linear approximation to the system dynamics equations and a steepest ascent extremum-seeking procedure. The procedure can also be reversed to determine design changes needed to give greater system stability. The applicability of the method for solving practical reactor problems has been demonstrated in an analysis of the Molten Salt Reactor Experiment using a computer program developed to implement the method. In this paper, the method is illustrated with a small sample problem.