We present a method for computing the stress intensity factors in bimaterials based on the goal oriented finite element error estimate. The goal oriented analysis focuses on computing the bounds on the local quantities of interest, e.g. local stresses, local displacements, stress intensity factors etc, of a structure, and with the bounds obtained on the coarse finite element mesh we can obtain the quantities of interest with nearly the same accuracy as that obtained on the fine finite element mesh. In this paper the stress intensity factors in bimaterials are first formulated as explicit computable linear function of the displacements by means of the two-points extrapolation method. Then the goal oriented finite element method is used to compute the lower and upper bounds on the stress intensity factors, and the average of the bounds is considered as a prediction of the stress intensity factor. At last, the stress intensity factors, 0 K and r K , in bimaterials are computed with the proposed method to show its efficiency.