A well plug for use in a subterranean well can include a generally tubular mandrel, a seal element positioned on the mandrel, and a setting rod releasably secured relative to the mandrel by an annular shaped shear ring or a bonded sleeve. The setting rod is releasable for longitudinal displacement relative to the mandrel in response to a predetermined shear force applied to the shear ring or bonded sleeve. A method of setting a well plug in a subterranean well can include displacing a generally tubular mandrel with a setting rod relative to an outer housing of the well plug, outwardly extending a seal element of the well plug in response to the displacing, and shearing a releasable attachment securing the setting rod relative to the mandrel, the releasable attachment comprising an annular shaped shear ring, or a bond between a sleeve and a surface.