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We describe the use of monolithic, buckled-dome cavities as ultrasound sensors. Patterned delamination within a compressively stressed thin film stack produces high-finesse plano-concave optical resonators with sealed and empty cavity regions. The buckled mirror also functions as a flexible membrane, highly responsive to changes in external pressure. Owing to their efficient opto-acousto-mechanical coupling, thermal-displacement-noise limited sensitivity is achieved at low optical interrogation powers and for modest optical (Q ~ 10^3) and mechanical (Q ~ 10^2) quality factors. We predict and verify broadband (up to ~ 5 MHz), air-coupled ultrasound detection with noise-equivalent pressure (NEP) as low as ~ 30-100 $μ$Pa/Hz^1/2. This corresponds to an ultrasonic force sensitivity ~ 2 x 10^-13 N/Hz^1/2 and enables the detection of MHz-range signals propagated over distances as large as ~ 20 cm in air. In water, thermal-noise-limited sensitivity is demonstrated over a wide frequency range (up to ~ 30 MHz), with NEP as low as ~ 100-800 $μ$Pa/Hz^1/2. These cavities exhibit a nearly omnidirectional response, while being ~ 3-4 orders of magnitude more sensitive than piezoelectric devices of similar size. Easily realized as large arrays and naturally suited to direct coupling by free-space beams or optical fibers, they offer significant practical advantages over competing optical devices, and thus could be of interest for several emerging applications in medical and industrial ultrasound imaging.