This paper presents a model for solving interface crack with arbitrary crack traction based on the Scaled boundary finite element method to study the significant influence of the traction acting on the crack faces on the stability of a crack. The order of stress singularity is complex for an interface crack. With the existence of crack traction, the stress singularity is more complicated. Base on the proposed model, stress and displacement are solved analytically in the radial direction, and the stress singularity at crack tip is obtained with high precision without refined mesh. The arbitrary crack traction is firstly decomposed to one component parallel to the crack and the other one perpendicular to the crack, then both the two components are expressed as the sum of a limited number of power functions respectively. The effect of each power function is solved analytically. According to the Linear superposition principle, the solution of a structure with arbitrary crack traction can be obtained. The proposed model is effective for both anisotropic and isotropic materials. The model is verified by several plates with crack tractions, in which stress intensity factors are calculated. Sensitivity analysis is also performed concerning the plate geometry and material properties. Finally the model is applied to solve the stress intensity factors of an interface crack of a gravity dam filled with water.