Determining safe regions of operation is important at the design, control and optimization of process systems. Process alarms and safety systems should be designed based on such knowledge. In classical control systems these regions are represented as independent constraints on process variables. In case of a highly exothermic reaction takes place in any kind of reactor there is a high risk to develop reactor runaway if the produced heat can’t be removed. Reactor runaway phenomena is a serious problem in many chemical industrial processes, hence the most of reactions are exothermic. Reactor runaway means a sudden and considerable change in process variables such as reactor temperature. To detect and forecast the development of runaway a model based criteria is introduced in this manuscript. The criteria is based on indirect Ljapunov’s stability analysis of a process model. The aim of this work is to compare methods for calculation of eigenvalues. Eigenvalues of the Jacobian matrix were calculated with a numerical method and there were also computed analytically. Stability of two-phases fed-batch reactor with highly exothermic reactions are analyzed with the investigated stability analysis methods. Analytical solution is more sensitive and of course it is more accurate than the numerical one still the algorithm based on the analytical solution is a lot more faster.