The density-functional theory (DFT) and density-functional perturbation theory (DFPT) are employed to study the electronic distributions and elastic properties of zinc-blende AlN and GaN. The linear charge density distributions along the [111] direction and charge density distribution of (001) planes for zinc-blende AlN and GaN are calculated. The total state of density and partial state of density of AlN and GaN are also calculated. Based on the optimized lattice parameters, the elastic constants and the internal strain parameters of zinc-blende AlN and GaN are calculated. The elastic tensors and compliance tensors are used to calculate Young’s modulus of (101) planes.