SnTe is a topological crystalline insulator that possesses spin-polarized, Dirac-dispersive surface states protected by crystal symmetry. Multiple surface states exist on the {100}, {110}, and {111} surfaces of SnTe, with the band structure of surface states depending on the mirror symmetry of a particular surface. Thus, to access surface states selectively, it is critical to control the morphology of SnTe such that only desired crystallographic surfaces are present. Here, we grow SnTe nanostructures using vapor-liquid-solid and vapor-solid growth mechanisms. Previously, SnTe nanowires and nanocrystals have been grown [Saghir et al. Cryst. Growth Des. 2014, 14, 2009-2013; Safdar et al. Cryst. Growth Des. 2014, 14, 2502-2509; Safdar et al. Nano Lett. 2013, 13, 5344-5349; Li et al. Nano Lett. 2013, 13, 5443-5448]. In this report, we demonstrate the synthesis of SnTe nanoplates with lateral dimensions spanning tens of micrometers and thicknesses of a few hundred nanometers. The top and bottom surfaces are either (100) or (111), maximizing topological surface states on these surfaces. Magnetotransport on these SnTe nanoplates shows a high bulk carrier density, consistent with bulk SnTe crystals arising due to defects such as Sn vacancies. In addition, we observe a structural phase transition in these nanoplates from the high-temperature rock salt to a low-temperature rhombohedral structure. For nanoplates with a very high carrier density, we observe a slight upturn in resistance at low temperatures, indicating electron-electron interactions.