<p>Contact problems widely exist in space engineering and their typical examples cover the space target capture mission, where the flexible cables and thin beams in the capture mechanism contact, collide and rebound against the surface of the rigid target. It is essential, hence, to numerically simulate the contact dynamics in order to ensure the capture success. In contact computations, the contact detection is usually the most time-consuming process to handle the contact problem. As such, this paper focuses on an accurate contact detection algorithm between flexible beams with circular cross-sections and a complex-shaped rigid body in the absolute coordinate formulation. The algorithm allows quick computation of the signed distance from the beam axis to the rigid surface via movable signed distance fields (SDF). The paper gives an efficient contact dynamics model of slender beams against a rigid body. Subsequently, it verifies the efficiency and accuracy of the model through numerical examples solved by the generalized-<i>α</i> algorithm. Finally, the paper presents numerical simulations of the contact dynamics of a tendon-actuated flexible capture system to validate the feasibility of the mechanism designed.</p>