This paper presents an approach to implement a sliding-mode position controller to a plant equipped with a nonsmooth actuator. The actuator is modeled as a setvalued function from the control input and the velocity to the actuator force, which is motivated by quasistatic characteristics of hydraulic actuators shown in a previous study. The implementation of the sliding-mode controller is performed with the implicit discretization of the nominal plant model and the controller, which copes with the difficulties caused by set-valuedness, such as numerical chattering. Stability analyses both in the continuous-time and discrete-time domains are presented. Simulation results illustrate the theoretical findings.