The theoretical calculations for the structural, thermodynamic, electrical and mechanical characteristics of aluminum and gallium were studied using ab initio principles. The Density Functional Theory (DFT) was used as the methodology, and it provides solutions to the Kohn – Sham equation. The elemental structures were obtained using Xcryden software, and the exchange correlation functions within the Perdew–Burke–Ernzerhof (PBE) functional were treated using the PAW pseudo–potentials and Generalized Gradient Approximation (GGA). The results obtained from the ab initio calculations engulfthat the structural properties of a(A), B(GPa), B’(GPa) and E(eV) for both elements studied. The parameters obtained for the mechanical properties C11, C12 and C44 were calculated for both metals. The elastic properties; G, B/G, E, μ, A and H were also calculated for both elements. The results obtained for aluminum shows the values of B, C’, C11, C12 and C44 are 45, 3.9, 50.20, 47.6 and 31 respectively. For gallium we obtained 47, 4.03, 52.373, 44.313 and 29.0 corresponding to B, C’, C11, C12 and C44 respectively.