This paper discusses the stability of the welding problems under different materials with same shearing modulus. Using the stability of Cauchy type integral while the smooth perturbation for the integral curve and Sobolev perturbation for the kernel density happening, the stability of complex stress functions are studied and errors of stress and displacement are given. This paper discusses the stability of the welding problems under different materials with same shearing modulus. The stability of Cauchy type integral while the smooth perturbation for the integral curve and Sobolev perturbation for the kernel density happening, the stability of complex stress functions are studied and errors of stress and displacement are given.