We theoretically study the phonons propagating through a superlattice consisting of alternating layers of an elastic solid and a fluid. In this structure, there exist phononic bandgaps not originating from Bragg reflections. We examine the origin of these non-Bragg gaps and show that they are peculiar to the solid-fluid superlattices, where the number of allowed modes varies periodically. Even a single solid layer immersed in fluid contains discrete frequencies at which incident waves are perfectly reflected. We demonstrate the resonant reflection process at these frequencies. In the multilayered structure, these transmission zeros are gathered and form a bandgap. This is similar to the relation between atomic levels and an electronic energy band, though the allowed and forbidden states are interchanged. This non-Bragg gap introduces novel degrees of freedom to the design of phononic bandgap structures. (C) 2016 The Japan Society of Applied Physics