Similar to the damage zone in the vicinity of faults, rock joints are composed of single or multiple fracture process zones, highlighting a high crack density and a decrease of Young’s modulus. Here specimens of limestone joint and granite joint were subjected to cyclic tensile stress of increasing amplitudes, up to failure. The cyclic tension tests were to study the elasticity and crack density adjacent to rock joints. Results show that the vast majority of tensile strain accommodates in the vicinity of rock joint, and rock joints have a nonlinear mechanical behavior during loading while a nearly linear behavior during unloading in the tensile stress-strain curves. A gradual reduction in Young’s modulus is seen with the increase of tensile strain. The cumulative crack damage after each stress cycle also induces a decrease in Young’s modulus. A stiffer response is found when switching from loading to unloading. During the unloading, a recovery in tensile strain and crack damage is observed, but some unrecoverable damage remains in the rock joint sample after each loading-unloading cycle. Based on the differential scheme, a constitutive model using two crack-related parameters, i.e., initial crack density and crack density increment, is developed. The model can give a micromechanical explanation and well reproduce the nonlinearity and hysteresis of tensile stress-strain curves.