In order to study the characteristics of acoustic/elastic wave propagation in one-dimensional (1D) solid-fluid periodic structure incited by omnidirectional incidence, a theoretical model of wave propagation in 1D solid-fluid periodic structure is established using a transfer matrix method. Based on this model, the band structures of the infinite case and the transmission properties of the finite one are further calculated and analyzed. The results show that an acoustic band fracture appears in the low frequency transmission zone for a certain incident angle. The corresponding incident angle of the fracture is non-relevant to the mass densities or the thicknesses of the solid and fluid layers constituting the periodic structure, and determined only by the wave velocity of the constituent material.