Spray jet in supersonic crossflows was investigated numerically using an Eulerian two-fluid model based on kinetic theory. Characteristic analysis was performed in three-dimensional condition to demonstrate the hyperbolic nature of the dispersed phase governing equations system. An SMD model was proposed according to the experimental data and incorporated into the simulations. Numerical tests were designed to explore the effects of droplet sizes on the predicted results. The penetration height and spray width were validated against the empirical correlations. The S-shaped distributions of the droplet velocity and Weber number were well described with the proposed SMD model, and good agreements with the experimental measurements were also achieved for the volume flux and droplet number density, respectively. The spray phase pressure reached its maximum near the bottom floor due to the high spray phase density there. The gas phase turbulence reduced the dissipation of the spray phase turbulent kinetic energy which was found growing below the middle height of the spray plume. (C) 2016 Elsevier Ltd. All rights reserved.