We study the existence of guided acoustic modes in layered structures whose phase velocity is higher than that of bulk waves in a solid substrate or an adjacent fluid half space, which belong to the class of bound states in the radiation continuum (BICs). We demonstrate that in contrast to the electromagnetic case, non-symmetry-protected BICs exist in isotropic layered systems without periodic structures. Two systems supporting non-symmetry-protected sagittally polarized BICs have been identified: (i) a supported solid layer yields BICs whose phase velocity is higher than the transverse velocity of the substrate but lower than the longitudinal velocity; (ii) a supported solid layer loaded by a fluid half space supports BICs whose velocity is higher that the bulk velocity of the fluid but lower than acoustic velocities of the substrate. The latter case is a unique example of BICs in the sense that it does not involve an evanescent field in the fluid half space providing the radiation continuum. In either case, BICs are represented by isolated points in the dispersion relations located within “leaky” branches. We show that these BICs are robust with respect to small perturbations of the system parameters. Numerical results are provided for realistic materials combinations. We also show that no BICs exist in all-fluid layered structures, whereas in solid layered structures there are no shear horizontal BICs and no sagittally polarized BICs whose velocity exceeds the longitudinal velocity of the substrate.United States. Department of Energy (Grant DE-FG02-00ER15087)