Hydraulic fracturing treatments have become an indispensable part of well completion in shale gas field development. Shale formations often contain natural fractures and complex hydraulic fracture networks may form during a treatment. The complex fracture network is strongly influenced by the interaction between the hydraulic fracture and the pre-existing natural fractures. A criterion has been developed to determine whether a fracture crosses a frictional interface (pre-existing fracture) at non-orthogonal angles. This criterion is an extension of the one for orthogonal crossing originally developed by Renshaw and Pollard (1995). The dependence of crossing on the intersection angle is shown quantitatively using the extended criterion. The fracture is more likely to turn and propagate along the interface than to cross it when the angle is less than 90°. The validation of the criterion using laboratory experiments for various angles is described and discussed. When applied to laboratory experiments, good agreement between the criterion and experiments is observed for a wide range of angles. The criterion can be used to determine whether hydraulic fractures cross natural fractures under particular field conditions, and it has been incorporated in a hydraulic fracture model that simulates hydraulic fracture propagation in a natural fractured formation.