Malfunctioning satellites are generally non-cooperative tumbling objects. Due to their complex tumbling motion, it is essential to stabilize the target within an acceptable rotating range in the pre-capture phase. In contrast to contactless methods, contact methods based on flexible devices are efficient and can generate sufficient operating torque through flexible contact. However, accurate dynamic analysis of the operation is challenging because of two limitations. It is difficult to obtain a high-efficiency description of the large deformation arising from the operating process. Moreover, the contact between a flexible device and a tumbling object is hard to detect efficiently. This paper proposes a method for detumbling a free-floating rotating satellite; it uses a flexible rod to contact the solar array of the target. The absolute nodal coordinate formulation is first applied to a rod-contact detumbling model in simulation to describe the large deformation of the rod precisely with a low computational burden. Next, a two-step method to detect the contact is employed to pinpoint the contact point and speed up the simulation: coarse detection in the contactless phase and fine detection in the contact phase. Finally, the feasibility of the contact detumbling method is verified. In addition, through the further analysis of the contact process, some characteristics of this kind of strategy are studied for the first time.