Probabilistic failure risk analysis is frequently used in the airworthiness area, while efficient stress intensity factor (SIF) solutions are vital in its process. Universal weight function (UWF) is a method that has remarkable computational efficiency and high accuracy in SIF calculation. However, the concrete coefficients in the UWF for different geometries remain unknown, which hinders the subsequent application of the method. This article focuses on general off-center embedded cracks. The response surface method is used to construct the UWF database. The accuracy of the database is confirmed by comparing it with existing literature and the finite element method, although large errors are identified to be inevitable for certain stress. Gaussian process regression is further adopted for better fitting, and the R-square is over 0.96. In addition, the effect of the offset distance on SIFs is discussed for embedded cracks in a given plate. Results show that SIF changes are dependent on the plate boundary in the uniform stress field, while stress predominates the SIF changes in nonuniform stress fields.