[en] The influences of doping on electronic structures and mechanical properties of BaHfO₃ are investigated by using first-principles plane-wave density functional theory within the generalized gradient approximation (GGA). The electronic structure calculations show that the lattice constant of optimized BaHfO₃ agrees with the experimental value, and BaHfO₃ and doped BaHfO₃ with Sr or Ti are both indirect band gap materials. Specifically, the band gap of Ba_0.5 Sr_0.5 HfO₃ increases and the characteristics of insulator enhances, while the band gap of BaHf_0.5 Ti_0.5O₃ is obviously reduced and the features of semi conductor material are displayed. The analysis of the density of states shows that the change of the band gap after doping is due mainly to the movement of the bottom of conduction band. The analysis of mechanical properties indicates that the shear modulus and Young's modulus of Ba_0.5 Sr_0.5 HfO₃ decrease comparing with BaHfO₃, which leads to the decrease of the hardness of the material. But for BaHf_0.5 Ti_0.5O₃, both the shear modulus and Young's modulus increase, which causes the enhance of hardness. Electron density distribution analysis reveals that the doping changes the valence electron concentration distribution of the system, resulting in the change of bonding characteristics of BaHfO₃, and this is the underlying reason for the change of hardness of the material. Thus, the doping can effectively control the hardness of the system. The results of the study provide a theoretical basis for the design and application of doping BaHfO₃ electromechanical materials. (authors)