Two-pass orbital rotary flanging is performed and the value of critical contact area ratio X_c during orbital rotary flanging is experimentally determined. In the two-pass orbital rotary flanging, 1050 aluminum and 5052 aluminum alloy tube-ends are conical flared using a tool in the first pass and then subjected to orbital rotary flanging in the second pass. The experimental results indicate that the values of the tilt angle of the tool ω₂ and the non-dimensional tool feed F significantly affect the prevention of curling and that the initial contact area ratio X₀ is the principle factor in the prevention of curling; the curling is prevented by setting X₀ below X_c. In addition, it is also experimentally found that X_c increases with increasing F for F<0.1; however, the rate of increase gradually decreases and X_c becomes constant (0.05) for F≥0.1.