The stability analysis of passive bolt-reinforced rock slopes under seismic loads is investigated within the framework of the kinematic approach of limit analysis theory. A pseudo-static method is adopted to account for the inertial forces induced in the rock mass by seismic events. The strength properties of the rock material are described by a modified Hoek–Brown strength criterion, whereas the passive bolts are modeled as bar-like inclusions that exhibit only resistance to tensile-compressive forces. Taking advantage of the ability to compute closed-form expressions for the support functions associated with the modified Hoek–Brown strength criterion, a rotational failure mechanism is implemented to derive rigorous lower bound estimates for the amount of reinforcement strength to prevent slope failure. The approach is then applied to investigating the effects of relevant geometry, strength and loading parameters in light of a preliminary parametric study. The accuracy of the approach is assessed by comparison of the lower bound estimates with finite element limit analysis solutions, thus emphasizing the ability of the approach to properly predict the stability conditions and to capture the essential features of deformation localization pattern. Finally, the extension of the approach to account for slipping at the interface between reinforcements and surrounding rock mass is outlined.