The use of two-phase ejectors to improve refrigeration systems encounters today a great interest. However, modeling of such devices with low void fraction at the entrance of the motive nozzle, presents significant challenges. The choking conditions and the discontinuities appearing in a two-phase flow in a nozzle are not well documented and some works are needed to better anticipated flow behavior under these conditions. This paper presents a steady state two-phase flow model including new choking criterions for one-dimensional conservative systems. The present model is a two-fluid, one pressure model with thermal equilibrium and mechanical disequilibrium. As a first step, this model is used to study the flow in the motive nozzle of an ejector.