Based on the first-principles method, the effects of pressure and temperature on the physical properties of Nbsub.2Bsub.3 and Tasub.2Bsub.3 were discussed. The approximate linear increase in B, G, and E with pressure was observed for Nbsub.2Bsub.3 and Tasub.2Bsub.3 with a minor difference for bulk modulus and similar values for shear and Young’s modulus. Nbsub.2Bsub.3 shows higher Vickers hardness and similar fracture toughness as compared with Tasub.2Bsub.3. An abnormal phenomenon of the simultaneous increase in hardness and B/G (σ) with the increased pressure was observed. The strong anisotropies of bulk, Young’s, and shear modulus were observed, and the differences of anisotropy between Nbsub.2Bsub.3 and Tasub.2Bsub.3 increased with pressure. At low temperatures, the α of Nbsub.2Bsub.3 is smaller than that of Tasub.2Bsub.3, but is larger than that of Tasub.2Bsub.3 at high temperatures. The Θ of Nbsub.2Bsub.3 are larger than those of Tasub.2Bsub.3 under the same conditions. The combination of relatively high Vickers hardness and fracture toughness is determined by the metallic bond and covalent bond. With the increased pressure, Nbsub.2Bsub.3 possesses the greater strength of B–B bonds than Tasub.2Bsub.3, which leads to its high hardness and Debye temperature.