Bridged or caged polycyclic hydrocarbons have rigid structures that project substituents into precise regions of 3D space, making them attractive as linking groups in materials science and as building blocks for medicinal chemistry. The efficient synthesis of new or underexplored classes of such compounds is, therefore, an important objective. Herein, we describe the silver(I)-catalyzed rearrangement of 1,4-disubstituted cubanes to cuneanes, which are strained hydrocarbons that have not received much attention since they were first described in 1970. The synthesis of 2,6-disubstituted or 1,3-disubstituted cuneanes can be achieved with high regioselectivities, with the regioselectivity being dependent on the electronic character of the cubane substituents. A preliminary assessment of cuneanes as scaffolds for medicinal chemistry suggests cuneanes could serve as isosteric replacements of trans-1,4-disubstituted cyclohexanes and 1,3-disubstituted benzenes. An analogue of the anticancer drug sonidegib was synthesized, in which the 1,2,3-trisubstituted benzene was replaced with a 1,3-disubstituted cuneane.