In this study, thermoacoustic analysis model was developed in order to predict both eigenfrequencies and initial growth rate of combustion instabilities for lean premixed gas turbine combustors. As a first step, a model combustor and nozzle were selected and analytical linear equations for thermoacoustic waves were derived for a given combustion system. Then, methods showing how the equations can be used for analysis of the combustion instability were suggested. It was found that the prediction results showed a good agreement with the measurements. However, there were some limitation in growth rate predictions, which were related with over-simplification of flame structure, acoustic boundary conditions, and temperature distribution in the combustor.