The structural, elastic, and thermal characteristics within the 0–30 GPa pressure range of Al3Ni intermetallic compounds were extensively studied using first-principles computational techniques. Using structural optimization, lattice parameters and the variation in volume variation under diverse pressures were determined, and the trends in their structural alteration with pressure were identified. The computed elastic constants validate the mechanical stability of Al3Ni within the applied pressure range and show that its compressive stiffness and shear resistance increase rapidly with increasing pressure. The Cauchy pressure variation implies that the metallic nature of Al3Ni increases gradually with increasing pressure. Moreover, through analysis of Poisson’s ratio, the anisotropy factor, and the sound velocity, we ascertained that pressure attenuates the anisotropic attributes of the material, and Al3Ni exhibits more pronounced isotropic characteristics and mechanical homogeneity under high-pressure conditions. The substantial increase in the Debye temperature further suggests that high pressure fortifies the lattice dynamic rigidity of the material. This current research systematically elucidated the stability of Al3Ni under high-pressure conditions and the law of the transformation of it mechanical behavior, providing a theoretical foundation for its application under extreme circumstances.