Abstract: Reservoir develops discontinuities, such as faults, natural fractures and joints, which have significant influences on the propagation of hydraulic fractures. Especially in tight sand and shale reservoir, etc., natural fracture affects the network fractures after hydraulic fracture treatment. A series of hydraulic fracture tests are conducted to investigate the propagation in a rock with discontinuities under different in-situ stresses utilizing a tri-axial fracturing test system. The results show that the horizontal stress difference has a critical value (5~7 MPa), below which the hydraulic fracture cannot cross the discontinuities. The larger the both strike angle and stress contrast coefficient, the easier the hydraulic fractures cross the discontinuities. The weak relationship between strike angle of discontinuities and hydraulic fracture propagation is demonstrated. The hydraulic fractures need to accumulate enough energy for crossing the discontinuities. There is an obvious difference in the treatment curves between the crossing and no-crossing experiments. The peak pressure of the treatment curve decreases as the minimum distance (noted as DNF) between the center of hydraulic fractures and discontinuities in reservoir increases. The strike angle is a key factor for the propagation of hydraulic fractures compared with the dip angle of discontinuities. It is necessary to obtain occurrence of a discontinuity and in-situ stress around this discontinuity in order to predict the hydraulic fracture propagation in reservoir. According to the characteristics of the treatment curve, whether the hydraulic fracture crosses the discontinuity and to qualitatively calculate the DNF or not can be judged, and it is useful for oilfields to evaluate the effect of hydraulic fractures.