Abstract: The interaction between hydraulic fracture (HF) and natural fracture (NF) plays a significant role in hydraulic fracturing and can lead to complex fracture networks. Based on the theory of fracture mechanics, this paper presents an explicit expression criterion of given parameters. This criterion is intended to predict the infiltration, openness and slippage of HF after it encounters NF, and to assess the results of existing hydraulic fracturing tests prior to conducting numerical simulations, experiments or field treatments. The criterion shows that HFs tend to penetrate NFs only under high differential horizontal stresses and high approach angles, while open NFs under lower differential horizontal stresses and lower approach angles. When the differential horizontal stresses, intersection angle and friction coefficient are appropriate, NFs will slip due to shear. In addition, high fracture toughness of rock and short HF length (distance between wellbore and NF) can also cause HF to open NF. Comparing with other implicit expressions or those given by computational programs, the proposed criterion relies only on external parameters, with explicit expressions to facilitate fracturing experiments and engineering applications.