An enhancement of the piezoelectric properties of lead-free materials, which allow conversion of mechanical energy into electricity, is a task of great importance and interest. Results of first-principles calculations of piezoelectric/electromechanical properties of the Ba(1-x)SrxTiO3 (BSTO) ferroelectric solid solution with a perovskite structure are presented and discussed. Calculations are performed within the linear combination of atomic orbitals (LCAO) approximation and periodic-boundary conditions, using the advanced hybrid functionals of density functional theory (DFT). A supercell model allows the investigation of multiple chemical compositions x. In particular, three BSTO solid solutions with x = 0, 0.125, 0.25 are considered within the experimental stability domain of the ferroelectric tetragonal phase of the, solid solution (x < 0.3). The configurational disorder with x = 0.25 composition is also investigated explicitly considering the seven possible atomic configurations corresponding to this composition. It is predicted that Sr-doping of BaTiO3 makes it mechanically harder and enhances its electromechanical/piezoelectric properties, which are important for relevant applications.