An Eulerian approach with mixed-fluid treatment has been used to study the flow field of an annular liquid jet in a compressible gas medium. A mathematical formulation is developed which is capable of representing the two-phase flow system with the gas phase treated as compressible and liquid as incompressible, where the volume of fluid method has been adapted to take into account the gas compressibility. The mathematical formulation is then applied to the computational analysis of an annular liquid jet, in order to achieve a better understanding on the flow physics by providing detailed information on the flow field. The gas-liquid two-phase flow system has been examined by direct solution of the governing equations using highly accurate numerical schemes. The numerical simulation shows that the dispersion of the annular liquid jet is characterised by a recirculation zone adjacent to the nozzle exit. Without applying perturbation at the domain inlet, vortical structures develop at the downstream locations of the flow field due to the Kelvin-Helmholtz instability. The flow becomes more energetic at progressive downstream locations with the dominating frequencies becoming smaller.