The structure, elastic properties, and thermodynamic properties of cubic boron arsenide (c‐BAs) under high temperature and high pressure are studied based on first‐principles calculations. The obtained equilibrium structure and mechanical properties are in good agreement with other theoretical results. First, the phonon dispersion spectra at zero pressure and high pressure are calculated. The results show that c‐BAs is dynamically stable under pressure of 0–110 GPa. Second, the lattice constants, elastic constants, Young's modulus, bulk modulus, shear modulus, Poisson's ratio, B/G, sound velocity, and Debye temperature of c‐BAs under zero pressure and high pressure are calculated. c‐BAs are predicted to be unstable above 112.3 GPa in accordance with the elastic stability criterion. Furthermore, it is indicated by the calculated B/G ratio that c‐BAs is brittle at zero GPa and begins to tend to be ductile as pressure rises to 46.4 GPa. The calculated elastic anisotropy coefficients indicate that c‐BAs has elastic anisotropy. The thermodynamic properties of c‐BAs are investigated at high temperatures and pressures by combining generalized density function theory and the quasiharmonic Debye model. It is suggested by the calculated elastic and thermodynamic properties that c‐BAs can be used as candidate structures for the fabrication of efficient solar cells and thermoelectric materials.