Rock joints play an important role in the behavior of rock masses under normal and shear loading conditions. Numerical simulation of the behavior of jointed rock masses is not an easy task due to complexities involved in the problem such as joint roughness, joint shear strength, hardening and softening phenomenon and mesh dependency. In this study for modeling purposes, a visco-plastic multilaminate model considering hardening and softening effects has been employed. For providing the necessary data for numerical simulation, a series of laboratory experiments have been carried out on regular tooth-shape asperities made by gypsum, under constant normal load conditions. Shear stress-shear displacement and normal displacement-shear displacement of artificial joint specimens are simulated using the proposed numerical model at constant normal load condition (CNL). The results indicate the capability of the model for simulating rock joints behavior in both strength and deformation field. Although the numerical model has been developed for simulating the behavior of artificial joints, the concept of the method can also be used for natural rock joints.