A numerical methodology for investigating compressor instabilities in a multistage environment is presented. The method is based on a stage-by-stage dynamic compression model and considers air compressibility explicitly throughout the compressor. It involves discretizing the compression system into distinct elements and a use of the local elemental characteristic of mean performance. The models are presented in both nonlinear and linearized forms. The linearised form permits well surge condition prediction for multistage axial compressors, while the non-linear form is able to investigate the growth of local flow disturbances, and helps to develop practical control strategy. Validations were carried out using the data from several aircraft engine compressors. A good experiment-model consistency is achieved.