The slipping effect during creeping flow of viscoplastic fluids around a circular cylinder has been investigated via numerical simulations. For the bulk behavior of the fluid, a Herschel–Bulkley law is considered. For the parietal behavior, an original and recent slip law based on an elastohydrodynamic lubrication model defined with a physical approach has been implemented. In particular, this law represents the behavior of Carbopol gels, which are commonly used during experimental studies on yield stress fluid mechanics and in industry. This law has two parameters that control the kinematic conditions at the fluid–structure interface. Variations in the plastic drag coefficient are given as a function of these parameters. It has been shown in particular the decreasing of the drag coefficient when there is slipping at the fluid–structure interface. The kinematic field has been analyzed and the evolution of rigid zones is illustrated. Results are provided for different slipping conditions ranging from the no-slip to the perfect-slip (PS) case. The sheared zone becomes smaller so the flow is more and more confined due to the slip, which induces modifications on the rigid zones. Some of the results are compared with existing asymptotic plastic drag coefficients and experimental data.