A new experimental rig was devised to study the influence of surface roughness on the structural response of specially designed test samples shaped as semicircular arcs. The rig was designed to provide consistent testing conditions for samples with different levels of roughness. Special attention is paid to defining the roughness and global geometry of semicircular arcs formed from 0.8 mm thick stainless steel SS1.4301 sheets. Experimental samples are divided into three groups with respect to their arithmetic mean roughness values of 12 nm, 35 nm, and 670 nm. The obtained results show that the displacement and strain of arcs depend on the roughness of the contact surfaces. A significant instability in the response of polished arcs is observed.