Multistage heat pumps are one of the most efficient technologies for delivering heat at temperatures below 100°C, Thanks to their fairly high exergy efficiency. In the recent years the development of radial compressors mounted on gas bearings have unlock the possibility of a downsizing of multistage heat pumps to the capacity range of domestic applications. Such small scale multistage heat pumps are expected to have increased efficiency at nominal and part load conditions, to be fully hermetic and to be more compact thanks to their oil free operation and the use of dynamic machines. As a result of an industrial collaboration, an experimental two-stage heat pump with flash economizer was built and tested in a previous work. It used radial oil free compressors arranged on a single shaft rotating on gas bearings. A dynamic simulation model has been developed in order to better understand the behavior of the aforementioned prototype, as well as to preliminary test control strategies. As a result, a whole range of dynamic models, including the evaporator, condenser, flash economizer, and compressors were developed using the modeling and simulation software gPROMS. They rely on simple two and three zone models for the evaporator and condenser respectively. Zero dimensional models were used for the compressors, two different types of which were implemented. One is a volumetric compressor with a fixed built-in volume ratio, connected to an asynchronous electric motor the other one is a variable speed radial type based on a simplified compressor map deduced from experimental data. As much as possible, the aforementioned models have been inspired from components available in the base library of gPROMS. The results showed that a two stage heat pump based on quasi constant speed volumetric compressors poses problem at low temperature lift, when the top part of the cycle is degenerated, making it close to a single stage machine. The version with the dynamic compressors does not exhibit any problem of degeneration of the cycle, while having a better performance and load characteristic curve. Both systems showed an insensitivity of the performances to the charge of refrigerant due to the buffering effect of the flash economizer. As a conclusion, a simple dynamic model was developed for simulating various types of two-stage heat pumps with flash economizer. It confirmed the potential of performance improvement of radial compressors based heat pumps over volumetric ones.