The machining instability (chatter phenomenon) easily occurs when flexible parts are machined. This paper predicts the milling stability domain of the flexible part with multiple structure mode interaction induced by the cutting force. First, the dynamic milling process of a flexible part is modeled as a multiple modal degree-of-freedom mechanical model. Then, the full-discretization method is employed to calculate the stability boundary and the cases with different factors are compared, the simulation shows that the cutting position has the dominating effect on the stability analysis of the flexible part milling. The chatter experiment verifies the validity of the proposed method. The proposed method can be used to improve the machining efficiency of flexible parts in aerospace and power industries.