The evaluation of changes in shear resistance on soft (or weathered) rock joints under cyclic shear loads with constant normal load (CNL) and constant normal stiffness (CNS) significantly contributes to increasing the safety and stability of rock slopes and underground structures. In this study, a series of cyclic shear tests were conducted on simulated soft rock joints with regular (15°-15°, 30°-30°) and irregular (15°-30°) asperities under different normal stiffnesses (kn). The results indicated that the first peak shear stress increases with the increase inknup to the normal stiffness of the joints (knj). Beyondknj, no significant change was observed in the peak shear stress. The difference in peak shear stress between regular (30°-30°) and irregular joints (15°-30°) increases asknincreases. The minimum difference of peak shear stress between regular and irregular joints was observed (8.2%) under CNL and the maximum difference was found (64.3%) onknjunder CNS. The difference in peak shear stress between the first and subsequent cycles significantly increases as both the joint roughness andknincreases. A new shear strength model is developed to predict peak shear stress of the joints for differentknand asperity angles under cyclic shear loads.