In this study, pull-out tests of blind rivet nuts (BRNs) mounted on cold-formed square hollow section (SHS) bodies with 100×100 mm nominal cross-section dimensions and different wall thicknesses (2.0 to 5.0 mm) were performed, and the effect of different wall thicknesses on the test results was experimentally investigated. M10 and M12 stainless steel BRNs were mounted on SHSs using a standard riveter tool, and the test elements were prepared for the experiment. Load–displacement curves and the final damage modes were obtained for each test specimen. The results show that the pull-out capacity depends on both the SHS wall thickness and rivet nut thread size. Although the pull-out capacity increased in both thread sizes with the increase in wall thickness parameters, the effect of thread size is negligible in the case of 2.5, 3.0, and 4.0 wall thickness. In addition, when a connection is created using a BRN, the design should consider the stripped thread strength in addition to the pull-out capacity.