We report on high-field (up to 30 T) magnetotransport experiments in topological crystalline insulator (111) SnTe epitaxial films. The longitudinal magnetoresistance ${R}_{\mathrm{xx}}$ exhibits pronounced Shubnikov--de Haas (SdH) oscillation at 4.2 K that persists up to 80 K. The second derivative $(\ensuremath{-}{d}^{2}{R}_{\mathrm{xx}}/d{B}^{2})$ versus $1/B$ curve shows a clear beating pattern and the fast Fourier-transform analysis reveals that the SdH oscillations are composed of two close frequencies. As SnTe has elongated bulk Fermi ellipsoids, the $1/cos\ensuremath{\theta}$ dependence obtained in the angular evolution of both SdH frequencies is not sufficient to assure conduction via surface states. The Lifshitz-Kosevich fitting of the ${R}_{\mathrm{xx}}$ oscillatory component confirms the two frequencies and enables us to extract the Berry phase of the charge carriers. The most likely scenario obtained from our analysis is that the beating pattern of these quantum oscillations originates from the Rashba splitting of the bulk longitudinal ellipsoid in SnTe.