© 2014 Optical Society of America. Three-mode optoacoustic parametric amplifiers (OAPAs), in which a pair of photon modes are strongly coupled to an acoustic mode, provide a general platform for investigating self-cooling, parametric instability and very sensitive transducers. Their realization requires an optical cavity with tunable transverse modes and a high quality-factor mirror resonator. This paper presents the design of a table-top OAPA based on a near-self-imaging cavity design, using a silicon torsional microresonator. The design achieves a tuning coefficient for the optical mode spacing of 2.46 MHz/mm. This allows tuning of the mode spacing between amplification and self-cooling regimes of the OAPA device. Based on demonstrated resonator parameters (frequencies ∼400 kHz and quality-factors ∼7.5 × 105) we predict that the OAPA can achieve parametric instability with 1.6 μWof input power and mode cooling by a factor of 1.9 × 104with 30 mW of input power.