In this doctoral thesis, advanced numerical model for analysis of power system angle stability is developed. The developed numerical model is based on a finite element technique (FET) procedure and time-varying phasors. Complex numerical analysis is performed simultaneously both in the time-domain and in the frequency-domain. In contrast to existing transient stability programs (TSP) that are limited to the first swing stability analysis, the developed numerical model can analyze long-term stability. The basis of developed numerical model for analysis of power system angle stability is application of finite element technique to the power system so that the considered system is divided into smaller parts, which are treated as separate finite elements (FE) with a certain number of local nodes during entire time-domain simulation. As the essential part of the power system, in the first step, a subtransient numerical model of the synchronous generator with the corresponding local system of algebraic equations that are obtained in frequency-domain is developed. The synchronous generator is defined and treated as a finite element with three local nodes. The time-domain model of turbine governor as well as excitation system has been also developed and incorporated into synchronous generator FE model for analysis of power system angle stability. Based on the corresponding mathematical models, numerical models of other parts of the power system (transformers, power lines, equivalent sources) have been also developed, which are treated as separate FE during entire time-domain simulation. The accuracy of the developed numerical model for analysis of power system transient stability is confirmed by comparing its computation results with results obtained by software package EMTP. The proposed numerical model enables a very simple and fast analysis of large power system angle stability.