Ejectors are among the widely used equipment in industry. The equipment name resembles its application in extracting a process fluid or an unwanted fluid from a system. Ejectors are used in applications such as power generation, oil and gas industries and refrigeration cycles. Simulation methods for ejectors are categorized into thermodynamic and dynamic methods. The present research investigates both methods in two phase flows without mass transfer effects. The present research also includes case studies of gas-gas ejectors and gas-liquid ejectors. In thermodynamic simulation of gas ejector, a modification to the traditional approach (e.g. former model of Huang) has been done and the result is compared against Huang's result and experimental data. The present prediction shows a better agreement with the experimental data compared to Huang's result. The error in entrainment ratio is about 1.4% and in area ratio is about 1.2%. In the CFD simulation of single phase flow ejectors, a gas-gas supersonic flow ejector with variable fluid properties has been simulated. It is shown that considering constant physical properties in this simulation may results in different predictions, as compared to considering variable properties. The latter gives more accurate predictions as temperature changes drastically along the ejector length and the temperature dependent properties vary considerably in the flow field. In studying two-phase ejectors, a water-air ejector is considered for thermodynamic analysis, as well as CFD simulation. The thermodynamic analysis assumes isentropic flow before and after the shock in the ejector. The thermodynamic model of Witt was modified by implementing a complete set of conservation equations of mass, momentum, energy, and entropy. Results indicate that the present model is superior to that of Witt. In the present model, there is no need to assume a tuning factor for the momentum equation, as it is naturally taken into account by considering the complete set of governing equation. The CFD simulation of this ejector was performed by the Fluent software. Numerical predictions show that by increasing the ejector outlet pressure, the entrainment ratio is increased. In order to assess the role of slip velocity in the prediction results, another slip model has been implemented into the code. The simulation with new slip model does not show considerable changes in the results. Therefore, it is recommended that the default slip model of Fluent be used in the simulations. Furthermore, a parametric study has been performed to study the effect of the bubble diameter on the simulation results. Different models for the bubble characteristic length are used in the computational code, and numerical simulations of the aforementioned two-phase ejector with these models are performed. Most of the models do not yield a converged result, and the results of those that converge were not encouraging. Therefore, a constant value for the bubble diameter has been used in simulation. In order to investigate the sensitivity of the simulation results to the bubble diameter, different values for the bubble diameter are used in the simulations. Numerical experiments with these different values show that the final simulation results are not affected appreciably by the value of bubble diameter. Keywords:Ejector, Thermodynamic dynamic analysis of ejector, Shock