Light-sheet fluorescence microscopy has revolutionized biology by visualizing dynamic cellular processes in three dimensions. However, light scattering in thick tissue and photobleaching of fluorescent reporters limit this method to studying thin or translucent specimens. In this study, we applied nondiffractive ultrasound beams in conjunction with a cross-amplitude modulation sequence and nonlinear acoustic reporters to enable fast and volumetric imaging of targeted biological functions. We reported volumetric imaging of tumor gene expression at the cubic centimeter scale using genetically encoded gas vesicles and localization microscopy of cerebral capillary networks using intravascular microbubble contrast agents. Nonlinear sound-sheet microscopy provides a ~64× acceleration in imaging speed, ~35× increase in imaged volume, and ~4× increase in classical imaging resolution compared with the state of the art in biomolecular ultrasound.