Surface acoustic waves (SAWs) in the GHz frequency range are exploited for the all-elastic excitation and detection of ferromagnetic resonance (FMR) in a ferromagnetic-ferroelectric (Ni/LiNbO(3)) hybrid device. We measure the SAW magnetotransmission at room temperature as a function of frequency, external magnetic field magnitude, and orientation. Our data are well described by a modified Landau-Lifshitz-Gilbert approach, in which a virtual, strain-induced tickle field drives the magnetization precession. This causes a distinct magnetic field orientation dependence of elastically driven FMR that we observe in both model and experiment.