Empowering independent control of optical and acoustic modes and enhancing the photon-phonon interaction, integrated photonics boosts the advancements of on-chip stimulated Brillouin scattering (SBS). However, achieving acoustic waveguides with low loss, tailorability, and easy fabrication remains a challenge. Here, inspired by the optical anti-resonance in hollow-core fibers and acoustic anti-resonance in cylindrical waveguides, we propose suspended anti-resonant acoustic waveguides (SARAWs) with superior confinement and high selectivity of acoustic modes, supporting both forward and backward SBS on chip. Furthermore, this structure streamlines the design and fabrication processes. Leveraging the advantages of SARAWs, we showcase a series of breakthroughs for SBS within a compact footprint on the silicon-on-insulator platform. For forward SBS, a centimeter-scale SARAW supports a large net gain exceeding 6.4 dB. For backward SBS, we observe an unprecedented Brillouin frequency shift of 27.6 GHz and a mechanical quality factor of up to 1960 in silicon waveguides. This paradigm of acoustic waveguide propels SBS into a new era, unlocking new opportunities in the fields of optomechanics, phononic circuits, and hybrid quantum systems.