In this study, a series of laboratory tests were conducted using a hydraulic fracturing system on the cement block specimens to investigate the hydraulic fracturing propagation and interaction with pre-existing fracture under true tri-axial stresses regime. The pre-existing fracture was prepared with different dip and strike angles in the test blocks. The Experimental results demonstrated two basic types of hydraulic fracture propagation in interaction point with pre-existing fracture, crossing and no crossing modes. They can be clearly identified from the relationships among strike angle, dip angle and in situ stresses. Two empirical relationships were proposed to describe the interactions between the pre-existing and hydraulic fractures. These relationships can be useful to predict the hydraulic fracture propagation behavior in naturally fractured reservoirs, although its accurate determination requires the more experimental and theoretical studies.