The paper investigates the effect of welding mode parameters on the uniformity of the deformation capacity of AISI 316 austenitic steel samples, namely, the influence of the welding current and purging gas consumption on the samples’ ability to perceive the force of cold cupping. Punch diameters of 3 and 8 mm were employed for the Erikson test to establish the dependence of the purge gas flow rate on the depth of the hole before the formation of cracks. The conducted metallographic studies confirmed an increase in the homogeneity of the dendritic structure in the weld zone due to the redistribution of heat input, as well as the absence of uneven grains and a decrease in the spread of grain sizes, which were in the range of 0.068–0.045 mm. The study resulted in determining the optimal range of technological parameters for the manufacture of flexible expansion elements to ensure their high operational properties.