In this doctoral thesis, an advanced numerical model for the analysis of angular stability in the power system (PS), which is based on the finite element technique and time-varying phasors, has been developed. The complex numerical analysis is simultaneously performed in both the time and phasor domains. The developed numerical model, unlike existing programs for the analysis of angular stability that are limited to the analysis of transient stability during the first quarter of the period, can analyze the entire transient phenomenon. The basis of the developed numerical model for the analysis of angular stability in the PS is the application of the finite element technique to the PS so that the considered system is divided into smaller parts, which are treated in the calculation process as separate finite elements with a certain number of local nodes. As the most important part of the power system, in the first step, a subtransient numerical model of a synchronous generator with an appropriate system of algebraic equations has been developed, which is defined and treated as a finite element with three local nodes. The developed numerical model of a synchronous generator for the analysis of angular stability in the power system includes the originally developed numerical model of a digital turbine controller as well as the originally developed numerical model of a digital voltage regulator. Also, based on the appropriate mathematical models, numerical models of other parts of the power system (transformers, lines, equivalent network) were developed, which were treated as separate finite elements in the calculation process. The accuracy of the developed numerical model for the analysis of angular stability in the power system was confirmed by comparing the calculation results with the results obtained using the EMTP software package. The proposed numerical model enables a very simple and fast analysis of the angular stability of a large power system.