Hydraulic fracturing is an effective method for developing unconventional reservoirs. The fracture height is a critical geometric parameter for fracturing design but will be limited by a weak interface. Fracture containment occurs when fracture propagation terminates at layer interfaces that are weaker than the surrounding rock. It always occurs in multilayer formation. Therefore, the mechanism of fracture height containment guides fracture height control in hydraulic fracturing. In order to study the fracture containment mechanism, this paper first calculates the propagation behaviour of the fracture in 3D under the influence of a weak interface through a block discrete element method and analyzes the geometric characteristics of the fracture after it meets the weak interface. Then, the induced stress of the hydraulic fracture on the weak interface is calculated by fracture mechanics theory, and the mechanism of blunting at the fracture tip is explained. Then, two kinds of interface slippage that can lead to blunting of the fracture tip are discussed. Based on the behavior of shear slippage at the interface, a control method for multilayer fracturing in thin sand-mud interbed and pay zone fracturing in shale is proposed. The results show that the fracture height is still limited by the weak interface in the formation without the difference of in-situ stress and rock properties. Interface slippage is the main factor impeding fracture propagation. Fracture height containment can be adjusted and controlled by changing the angle between the hydraulic fracture, the interface, and the stress state to strengthen and stiffen the interface. This study has a certain guiding significance for fracture height control in the design of hydraulic fracturing of shale or thin sand-mud interbed reservoirs.