The propagation of elastic flexural gravity waves through an ice shelf is modeled by two full 3D finite‐difference elastic models that are coupled to a treatment of undershelf sea water flux. These models are based on the momentum equations written using the well‐known differential equation form (model 1) and using an integro‐differential form (model 2). The integro‐differential form works with a variable that represents the vertical integration of the momentum equations from the current vertical position to the ice surface. The sea water flow under the ice shelf is described by a wave equation involving the pressure. Numerical experiments were undertaken for an ice shelf with spatially periodic crevasses. These experiments reveal that band gaps occur in the dispersion spectra in frequency bands that are consistent with Bragg’s law. It is found that the minimum threshold of crevasse depth must be exceeded for band gaps to arise. In particular, model 2, based on the depth‐integrated momentum equations, provides the smaller averaged (in the considered range of the spatial periodicities of the crevasses) threshold value.