This master thesis deals with the numerical simulation of incompressible, turbulent, two-dimensional flow in the cascades of an axial air turbine. The goal is to calculate the individual characteristics of the guide row and rotor row. More specifically, these are the exit flow angle and the total pressure coefficient depending on the inlet flow angle. Further are the wake and the static pressure distribution examined. The numerical simulation of the turbine stage based on the Mixing-Plane-Method is used to determine the characteristic curve of turbine and the stage efficiency. Due to lack of measurement results at least the numerically determined loss coefficients of the stator and rotor grid are verified with an analytical loss calculation. In this context, the theoretical foundations of axial turbine stages and the treatment occurring loss sources are summarized. A presentation of the modeling of turbulent flows with a focus on the boundary layer treatment is also available. The full Navier-Stokes equations are given, which form the basis for using CFD program ANSYS FLUENT. The essentials of some turbulence models are discussed, especially the Menter-modified k-w-SST model which is used to model the boundary layer and turbulence. The stator and rotor blades are created from existing data sheets. The calculation grid is meshed with the ICEM CFD program. The mesh topology, but most of all the boundary conditions are explained in detail. Those in ANSYS FLUENT implemented settings are also noted. Finally, there will be a graphical representation and analysis of the numerical results. For greater clarity, the stator and rotor simulations are treated separately. Also, a further reflection of the evaluation of the characteristic turbine curve and the stage efficiency is given. The calculations of the cascade characteristics and loss coefficients are carried out respectively at the blade hub, in the blade middle and at the blade tip.