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A computational method has been developed using finite volume method in conjunction with ALE (Arbitrary Lagrangian Eulerian) approach. The compressible, two-phase flow through the air-assisted injection system of a new, low-emission two-stroke engine under development is studied using this model. Good agreement is observed between computations and measurements of fuel consumption and pressure recovery in the air-assisted injection system of the current prototype. The crucial characteristics determining the performance of the injection system have been identified. The modeling shows possible reasons for the problems encountered by the prototype under certain operating conditions. Finally, the dependence of the performance of the injection system on certain crucial geometric parameters is studied. The present model would be a useful tool for the optimization of the overall system.