In the present study, mathematical modelling of different chamber profile of the vacuum pump to evaluate the evacuation time is developed. The validity of the developed mathematical modelling is demonstrated by performing an experiment on the vacuum pump with elliptical profile. The performance of the elliptical profile is also compared with that of the circular profile chamber of vacuum pump. It is shown that the evacuation time of vacuum pump with an elliptical chamber is lower than with a circular profile. Various parametric studies are also performed to investigate the effect of rotor eccentricity, ratio of minor and major axes of the elliptical profiles, air tank capacity on evacuation time of the vacuum pump.