A new method is presented to compute the Stress Intensity Factors(SIF) by combining analytical solutions with numerical solutions in previous studies based on numerical manifold method, which obtains optimal approximation at the crack tip but only for the type Ⅰ and typeⅡ cracks in planar. Following the idea of combined application, Williams series is introduced at the crack tip and 3D SIF for three-dimensional straight through cracks is completed via combining analytical covers with numerical covers, which obtains higher computational precision than other numerical methods. Meanwhile, the corresponding formulas of the stiffness matrix and the strain matrix are deduced，and numerical examples shows the validity of the method in solving the exact solution of 3D stress intensity factor.