Vapor compression cycles (VCS) based thermal management systems are being considered in modern aircraft where dynamic changes in heat loads are very common. Predicting dynamic behavior of vapor compression systems is critical to design, sizing, and control of aircraft thermal management systems. A novel Lagrangian method to model the dynamic behavior of vapor compression cycles is presented in this thesis. Fluid flowing through a vapor compression cycle is divided into a large number of material volumes (or mass elements). The mass contained in each element is fixed while the size of the material volume is allowed to change based on its density. At every time step, heat transfer to each mass element is determined and corresponding changes in the thermodynamic properties are evaluated. Each mass element is tracked as it moves through the evaporator, the compressor, the condenser, the expansion valve, and the piping connecting these components. This approach improves on previous models by accounting for spatial mass and enthalpy distribution, meaning that transport delays are reflected in the model result. The model predicts the transient variation during normal operation as well as start-up and shut-down modes. Model results were compared to experimental data at steady state. The model was then validated by comparing the predicted system behavior with experimental data. Results are presented and explained for three major operating condition variations : change in heat load, change in sink availability, and changes in system throttling via the expansion valve and compressor. The results depict extensive coupling of system parameters and significant response to exogenous inputs. The resulting model is modular, adaptable and runs cases faster than real time. Many opportunities exist for its utilization.