A method of installing fastening elements, and rivetless fasteners for use with the method. Rivetless nutplate fasteners are installed in metal structures by providing flush fit barrel shaped plug or bushing portions in a hole in the structure as defined by an edge wall. The barrel portion is acted upon axially, and expanded radially outward toward the edge wall of the hole, to provide an interference fit. The ends of the barrel portion are machined as desired for flushness. Also, a hole is installed as necessary. Rivetless nutplates are easily installed, and the installation enhances fatigue life of the hole surrounding the barrel of the nutplate.