The flowfield around a 6:1 prolate spheroid at angle of attack is predicted using solutions of the Reynolds-averaged Navier-Stokes (RANS) equations and detached-eddy simulation (DES). The calculations were performed at a Reynolds number of 4.2×106, the flow is tripped at x/L=0.2, and the angle of attack α is varied from 10 to 20 deg. RANS calculations are performed using the Spalart-Allmaras one-equation model. The influence of corrections to the Spalart-Allmaras model accounting for streamline curvature and a nonlinear constitutive relation are also considered. DES predictions are evaluated against experimental measurements, RANS results, as well as calculations performed without an explicit turbulence model. In general, flowfield predictions of the mean properties from the RANS and DES are similar. Predictions of the axial pressure distribution along the symmetry plane agree well with measured values for 10 deg angle of attack. Changes in the separation characteristics in the aft region alter the axial pressure gradient as the angle of attack increases to 20 deg. With downstream evolution, the wall-flow turning angle becomes more positive, an effect also predicted by the models though the peak-to-peak variation is less than that measured. Azimuthal skin friction variations show the same general trend as the measurements, with a weak minima identifying separation. Corrections for streamline curvature improve prediction of the pressure coefficient in the separated region on the leeward side of the spheroid. While initiated further along the spheroid compared to experimental measurements, predictions of primary and secondary separation agree reasonably well with measured values. Calculations without an explicit turbulence model predict pressure and skin-friction distributions in substantial disagreement with measurements.