Ab initio studies of structural, elastic and electronic properties of the tetragonal perovskite-type PbZr 0.5 Ti 0.5 O 3 are presented using the pseudo-potential plane wave method within the density functional theory in generalized gradient approximation. The calculated equilibrium lattice parameters remain in a good agreement with the available experimental data. The bulk modulus obtained from the Birch–Murnaghan equation of state is calculated as it B 0 =170GPa, and the gap energy E g =2.1–3.5eV. The some differences between calculated and nominal charges exist for all atoms. The biggest ones are on the Pb ions. They are caused by hybridization of the Pb 6s and O 2p states. The influence of the strain on the averaged over directions Young modulus in the 0.1–0.3% range was studied.