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This paper presents steady-state simulations of two-stage space transport systems during separation. The stage separation is simulated in quasi-steady-state flow so that there is no effect of a downwash due to the orbital-stage motion to be considered. The computational model of an orbital stage is set at various positions relative to a carrier stage. The simulations of stage separation considering time-dependent flow will be presented in a separate paper. For the steady-state simulation, two carrier-stage models are used: namely, a flat plate for simplifying interference effects and a fully detailed vehicle (elliptical aerodynamic configuration). In both cases, the orbital stage consists of a detailed configuration (elliptical aerodynamic configuration orbital stage). The steady-flow solutions are obtained by solving the three-dimensional Euler equations using the explicit finite volume shock-capturing method with the modified advection upstream splitting method approach for convective flux evaluation. The simulations are performed on structured multiblock grids with elliptic grid smoothing based on the Poisson equations. Flowfield patterns demonstrating strong interference effects due to incident and reflected shock waves and expansion regions as well as corresponding surface pressure distribution and aerodynamic forces and moments of carrier and orbital stages are analyzed. From the solutions for both configurations, good agreement is found comparing numerical and corresponding experimental results. Nomenclature C D = total drag coefficient C L = total lift coefficient C M = total pitching-moment coefficient C p = pressure coefficient F, G, H = fluxes in curvilinear and dimensionless coordinate system h KOS = distance from axis X EOS to the flat plate or distance from axis X EOS to axis X ELAC J = Jacobi matrix for the coordinate transformation L = reference length of elliptical aerodynamic configuration orbital stage M 1 = freestream Mach number P, Q, R = source terms of grid smoothing p = static pressure Q = state variables in the curvilinear and dimensionless coordinate system u, v, w = velocity components X, Y, Z = axes of the Cartesian coordinate system of the vehicle stage x, y, z = Cartesian coordinates = relative angle of attack , , = curvilinear coordinates = density