A numerical study of the aerodynamic and thermal environment associated with axial turbine stages is presented. Computations were performed using a modification of the unsteady viscous code, ROTOR1, and an improved version of the steady inviscid cascade system, MERIDL-TSONIC, coupled with boundary layer codes, BLAYER and STAN5. Two different turbine stages were analyzed: the first stage of the United Technologies Research Center Large Scale Rotating Rig (LSRR) and the first stage of the Space Shuttle Main Engine (SSME) high pressure fuel turbopump turbine. The time-averaged airfoil midspan pressure and heat transfer profiles were predicted for numerous thermal boundary conditions including adiabatic wall, prescribed surface temperature, and prescribed heat flux. Computed solutions are compared with each other and with experimental data in the case of the LSRR calculations. Modified ROTOR1 predictions of unsteady pressure envelopes and instantaneous contour plots are also presented. Relative merits of the two computational approaches are discussed.