This paper investigates the dynamics of a sinking winch mechanism in the framework of non-smooth dynamics. The previous works ignored the unilateral property of the cable (it can only pull the platform but can’t push it), which is specially taken into consideration in this paper. We propose the set-valued tension law to model the unilateral constraints of the cables. The equations of motion are derived by use of the Lagrange multiplier method. The dynamics model of the mechanism is obtained by combining the equations of motion and the set-valued tension law. Its solution is solved by the Moreau midpoint method. We present a numerical simulation study to demonstrate that the non-smooth dynamics framework is effective and suitable for the dynamic analysis of the sinking winch mechanism.