Slickwater hydraulic fracturing creates complex fracture networks in unconventional shale gas reservoirs. The use of spherical micron and nano-sized particles have been proposed as suitable sized materials to keep nano fractures conductive. Few materials have been investigated for occupying induced unpropped nano fractures. In this study, the nanomechanical properties of α-Al2O3, a commonly used fracture fluid nanomaterial is calculated using the density functional theory to study its pressure-dependent elasticity and hardness. The elastic properties of α-Al2O3 are calculated within the CASTEP code under different hydrostatic pressures between 0 and 1 GPa. α-Al2O3 experienced a 0.11 and 0.34 in structural lattice constant and volume, respectively. Material mechanical properties such as the Bulk modulus B, decrease Shear modulus G, Young's modulus and Poisson's ratio of the trigonal α-Al2O3 nanocrystal structure are derived through the Voight-Reus-Hill approximation scheme. Young's modulus of 391.8 and Hardness of 20.4 Gpa show that α-Al2O3 nanoparticles can withstand reservoir pressures without significant deformation. Elastic constants of α-Al2O3 generally increased with high pressure. However slight variations occurred in the derived nanomechanical properties between the pressure regime investigated. © Published under licence by IOP Publishing Ltd.