Semiconductur nano- and micropillars represent a promising platform for hybrid nanodevices. Their ability to couple to a broad variety of nanomechanical, acoustic, charge, spin, excitonic, polaritonic, or electromagnetic excitations is utilized in fields as diverse as force sensing or optoelectronics. In order to fully exploit the potential of these versatile systems e.g. for metamaterials, synchronization or topologically protected devices an intrinsic coupling mechanism between individual pillars needs to be established. This can be accomplished by taking advantage of the strain field induced by the flexural modes of the pillars. Here, we demonstrate strain-induced, strong coupling between two adjacent nanomechanical pillar resonators. Both mode hybridization and the formation of an avoided level crossing in the response of the nanopillar pair are experimentally observed. The described coupling mechanism is readily scalable, enabling hybrid nanomechanical resonator networks for the investigation of a broad range of collective dynamical phenomena.