The distribution and value of welding residual stress for 1Cr18Ni9 stainless steel stud welding joints was systemically simulated by ANSYS FE software. The mathematical estimating models of strength of the welded joints were established. Simulation results showed that the welding residual stress was tensile at the edge of the stud, while it was compressive stress at the position near axis center. The largest tensile stress did not exceed yield limit of material. The residual stress had more influence on the strength of welded joints.