The oil tank steel plate of the distribution transformer is covered with welds, and the fatigue failure of the oil tank often occurs in the internal defects of fillet welds. Given the above problems, this paper puts forward the bearing capacity calculation formula of cold-rolled steel plate and carries on the force analysis of steel plate and the fatigue analysis of weld through finite elements. Based on the theory of plastic limit design, the ultimate flexural bearing capacity of the control section of steel plate members is proposed. The calculation formula of equivalent structural stress is given based on the calculation method of structural stress and linear elastic fracture mechanics, and the calculation method of fatigue life and fatigue cumulative damage is given. Then, the elastic-plastic equation is solved according to three criteria: Mises yield criterion, plastic flow criterion, and strengthening criterion. Based on the above numerical simulation analysis, the mechanical model of steel plate weld is constructed, the mesh is divided, the boundary conditions are restricted and the same load is applied. ABAQUS analysis results show that the stress distribution curve of the connector has a maximum value at X = 80 mm and X = 210 mm, that is, the top surface of the connector steel plate has an obvious stress concentration at 80 mm and 210 mm. When the length of the weld is not more than 60 times the size of the welding foot, the full section of the core plate will yield, and the maximum stress value of the weld element will not exceed the tensile strength value of the welding material. The error of the results calculated by the formula in this paper is mostly within 10%, and the rest is basically within 20%. Therefore, the bearing capacity formula of the steel plate in this paper has ideal calculation accuracy and can provide effective guidance for the design of distribution transformer oil tanks.