The article is concerned with the development of an analytical method enabling the calculation of force used for the bending of a ring-shaped product during the butt welding allowing for the presence of plastic strains in the shunting zone. The research involved the investigation of principles governing the plastic-elastic strain of curvilinear bars subjected to bending and the development of theoretical foundations enabling the identification of displacements in such bars. The research-related investigation led to the obtainment of analytical equations combining bend force with movements of welding machine fixing clamps, geometrical parameters and physico-mechanical properties of a ring-shaped product material subjected to welding. Using a number of frames as an example, it was demonstrated that plastic strains significantly affected the value of bend force. The calculation results concerning the volume of bend force obtained using the above named analytical method converged with the results obtained using numerical calculations. Appropriate formulas were used to describe the boundaries of elastic and plastic areas of the shunting zone subjected to bending during butt welding. The research resulted in the determination of the critical value of bending force, the exceeding of which led to the deformation of the required geometrical shape of a ring-shaped product subjected to welding.