Using a recently developed first-principles approach tor determ1mng indentation strengm [Phys.Rev.Lett.98, 135505 (2007);ibid102, 055503 (2009)], we performed calculations of the ideal strength of hexagonal Re, Re3N, Re2N, Re2C, Re2B and ReB2 in various shear deformation directions beneath the Vickers indentor.Our results show that the normal compressive pressure beneath the indentor weakens the strength of these electron-rich rhenium boride, carbide and nitride compounds which belong to a distinct class of newly designed ultra-incompressible and ultrahard materials [,Science 308, 1268 (2005);ibid316,436 (2007)].The reduction of indentation strength in these materials stems from lateral bond and volume expansions driven by the normal compressive pressure mediated by the high-density valence electrons in these structures.We compare the calculated indentation strength to the Poissons ratio, which measures the lateral structural expansion, for the rhenium boride, carbide and nitride compounds as well as diamond and cubic boron nitride.Our analysis indicates that although the nommal pressure beneath the indentor generally leads to more significant reduction of indentation strength in materials with larger Poissons ratios,crystal and electronic structures also play important roles in determining the structural response under indentation.The present study reveals structural deformation modes and the underlying atomistic mechanisms in transition-metal boride, carbide and nitride compounds under the Vickers indentation.The results are distinctive from those of the traditional covalent superhard materials.The insights obtained from this work have important implications for further exploration and design of ultrahard materials.