This paper presents a novel technique for numerical analysis of electromagnetic transients and electromechanical oscillations in a power system. The proposed method is based on the finite element method (FEM). The finite element technique so far used for numerical analysis of continuum field problems here has been adopted to analyse electromagnetic and electromechanical transients in a power system. According to the finite element technique in the field problem, where the region of interest is divided into finite elements, in the proposed method power system is also divided into electric power system (finite) elements. Each finite element (generator, transformer, transmission line, load etc.) is characterized by a system of governing differential equations. Using generalized trapezoidal rule, also known as thetamethod for time integration, the system of differential equations of each electric power system (finite) element can be transformed to the system of algebraic equations for every time step. Once when a system of algebraic equations of each electric power system element is obtained, assembly procedure has to be done. The main contribution of the proposed approach is in an assembly procedure. With the proposed approach, in case of any disturbances in power system or in a part of power system, nodal voltage and branch currents will be obtained, as well as all other interesting variables. The proposed method will be tested on the example of the single-phase short circuit in the power system.