The symmetrical study is the most important mode of operation of a power system. This paper presents the Matlab applications to the solutions of the steady state and transient problems in power systems, including power flow studies, short circuit analysis and stability analysis. Here power system is modeled by an electrical network and solved for the steady-state powers where generator behaves more like power sources. Mainly 3 methods named Gauss-Seidel, Newton Raphson and Decouple methods are used for analyzing the above conditions. Its output is then used for analyzing the short circuit and stability analysis.