The finite-element approaches are used to the analysis of the properties of acoustoelectronic devices on surface acoustic waves (SAWs) made using thin-film technologies. The device consists of a barium titanate BaTiO3 film placed on a magnesium oxide substrate MgO. The barium titanate (BT) film is studied in the c-, r-, and aa-phases. The interdigital transducer (IDT) is attached to the free surface of the ferroelectric film and consists of a system parallel electrodes (pins) alternately connected to each other via common buses. The commercial software COMSOL is used for two-dimensional finite-element analysis and modeling the processes of excitation and propagation of SAW. The resonance and antiresonance frequencies are calculated for different film thicknesses and values of the lattice misfit strain. The significant influence of the film thickness and strains near the phase transitions and in r-phase on the resonant and antiresonant frequencies is discussed. In addition, a two-dimensional model of a SAW filter consisting of 40 pair pins of transmitting and receiving IDTs spaced 1.8 mm apart is considered. The frequency dependences of scattering parameters (S-parameters) have calculated and are presented.