The results of ab initio (first-principles) computations of structural, elastic and piezoelectric properties of Ba(1-x)SrxTiO3 (BSTO) and Ba(1-x)CaxTiO3 (BCTO) perovskite solid solutions are presented, discussed and compared. Calculations are performed with the CRYSTAL14 computer code within the linear combination of atomic orbitals (LCAO) approximation, using advanced hybrid functionals of the density-functional-theory (DFT). Supercell model allows us to simulate solid solutions with different chemical compositions (x = 0, 0.125 and 0.25) within ferroelectric tetragonal phases (x < 0.3) of both solid solutions. It is shown that configurational disorder has to be taken into account in simulations of BCTO solid solutions, while for BSTO this effect is rather small. Both BSTO and BCTO show significantly enhanced piezoelectric properties, in a comparison with pure BaTiO3. However, these solid solutions demonstrate opposite behaviour of a tetragonal ratio c/a and elastic constants as the functions of chemical composition. It is predicted that due to decrease of the elastic constants in BCTO, it has much higher converse piezoelectric constants than BSTO.