Being important for the antiresonance frequency tuning of tunable thin Film Bulk Acoustic wave Resonators (FBARs), the non-linear electrostrictive coefficient was for the first time calculated for BaTiO3 and SrTiO3 using ab initio methods. Further, taking into account the small difference of obtained values for BaTiO3 and SrTiO3 these results were linearly interpolated to the BaxSr1-xTiO3 (BST) compositions. The obtained values are consistent with previously made order-of-magnitude estimates. Using parameters obtained with first principles calculations, we simulated the resonance parameters of BST based tunable FBARs. Resulting antiresonance tuning was smaller than expected due to the compensation of two competing terms conditioned by linear and non-linear electrostrictions. Our calculations confirm that, for tunable FBAR modeling, it is important to use a polarization-based Landau free energy expansion taking into account both non-linear electrostriction and background permittivity. (C) 2013 AIP Publishing LLC.