The inter-area oscillation using eigenvalue method is presented and analyzed by modeling and linearizing the system around the operating point. This Thesis introduces the inter area oscillation using Eigen value method by presenting and discussing a proposed power system of two-area, 4-machine. The method of Eigen-analysis is utilized to perform the study of the inter-area oscillations with an emphasis on the oscillation mode with low frequency and light damping. The eigenvalues, eigenvectors, and participation factors associated with the inter-area oscillation modes are calculated in details and possible locations of power system stabilizer are chosen for study accordingly. This method is referred to as Eigen-value analysis (modal analysis) for small signal stability problem. It uses mathematical model to indicate whether the system is stable based on the eigenvalue calculation for the mathematical model. In this Thesis the application of modal analysis to inter-area oscillations study has been investigated. With the application of eigenvalue analysis on a test system it was possible to detect inter-area oscillations and determine how different parameters of the system influence them. Eigenvector and participation factor analysis has been shown as a powerful tool in detecting the oscillations and investigating factors that are influencing the small signal Stability. For a desired mode to be damped, the machine with the state that participates the most in that mode is the machine where the PSS should be installed. Therefore we can install the PSS in second area for cost effective point of view which damp the oscillation. Load flow calculations are used to analyze power systems under steady-state non-faulted (short-circuit free) conditions. Where steady-state is defined as a condition in which all the variables and parameters are assumed to be constant during the period of observation. To complete a modal analysis in using the default options in PowerFactory, we must follow the steps to use the toolbar selection button to choose the Modal Analysis toolbar and then We Calculate Initial Conditions using the button to open the command and then press Execute. The eigenvalue analysis is only available with balanced RMS simulation method. Note that the calculation of initial conditions needs a converging load-flow. If we want to quickly complete the modal analysis and capture all eigenvalues using the default options, we can press win the subsequent dialogue box and the calculation will proceed. When the calculation is complete we can view the Modal Analysis results.