The paper presents a numerical simulation of the transonic flow of steam with a non-equilibrium phase change. The flow of steam is approximated by a mixture model complemented by transport equations for moments. Proper formulation of the problem consists of domain definition, a complete set of equations, and appropriate choice of initial and boundary conditions. This problem is then solved numerically by a numerical code, that has been developed in-house. The code is based on a fractional step method and a finite volume formulation. Important issues related to numerical solution are discussed. Results for flow in a turbine are presented.