The interaction between a natural fracture (NF) and a hydraulic fracture (HF) has been studied extensively, both experimentally and numerically, to better understand the potential for crossing and arrest of a hydraulic fracture intersecting a natural fracture. However, the actual mechanical interaction between a hydraulic and a natural fracture or a bedding plane has not been studied, particularly under triaxial stress and injection conditions. Analysis of field microseismic data recorded during hydraulic fracturing shows that the bedding plane could slip due to the approaching hydraulic fracture. In this paper, we present the results of some lab-scale experimental work, demonstrating HF/NF interaction with an emphasis on the slippage of a discontinuity surface. Injection pressure, stress applied, and the sample deformation are monitored during the tests. Acoustic Emission (AE) technology is employed to record the AE signals generated during fracture initiation, propagation, and during the sliding of the joint. In addition, strain gauges are used to measure the slippage on the natural fracture. The tests are carried out on 101.6 mm diameter cylindrical samples of PMMA, shale, and granite. The calculated displacement based on the recorded strain clearly shows a jump at the breakdown point, which is accompanied by increased AE activity and stress drop. Analysis of the data clearly shows the occurrence of slippage on the joint in response to an approaching hydraulic fracture. Expectedly, the degree of shear slip varies with natural fracture dip and friction angle.