For the first time the structural, elastic and band gap properties of 10 perovskite crystals IAIIAF 3 (IA=K, Rb; IIA=Be, Mg, Ca, Sr, Ba) were calculated systematically using the CRYSTAL09 program. Several trends in the variation of these properties in relation to the Ionic radius R of the alkaline-earth metals ions were found. In particular, the lattice parameter of these compounds increases with R, whereas the elastic constants and band gap decrease. The Research of above properties will be very helpful in order to further improve their performances on the high-technology applications.