Steady (acoustic) streaming around a rigid oblate spheroid is studied in the incompressible limit when the fluid medium and the particle are in a small-amplitude high-frequency relative oscillatory motion along the symmetry axis of the spheroid. The inner (inside the thin Stokes shear-wave layer) and outer streaming patterns are analysed. A solution for the outer streaming is obtained analytically for small Reynolds numbers. At large Reynolds numbers, a boundary-layer consideration is carried out. Steady streaming in the disk limit, as approached within the family of oblate spheroids, is systematically investigated in the large Reynolds number case, and qualitative implications for shapes other than oblate spheroidal are discussed.