We present the numerical solution of the Euler equations of gas dynamics around the double ellipsoidal shape proposed by the organizers of the Antibes 1990 workshop. In two of the test cases we consider a modelization of air by a polytropic perfect gas, at an upstream Mach number M∞ = 8.15, and under incidences α = 0° and 30° (problems 6.1.5 and 6.1.7). The last test case is related to hypersonic regimes (M∞ = 25, α = 30°) and the air is therefore described as a real gas at chemical equilibrium (problem 6.3.9).