<p>This study investigates elastic instability-activated bandgaps for shear waves in soft laminates comprised of phases that exhibit stiffening. In particular, the Gent material model is used for phases. The stiff layer buckling, influenced by the stiffening behavior, results in a regulated wavy pattern along the layer direction. We analyzed how this phenomenon affects the shear wave propagation propagating along the buckled layers. Our findings exhibit that this reversible shift from an infinitely extended to a periodic structure modifies the dispersion relations and triggers shear wave bandgaps. We show that the frequency of the bandgap is closely related to the buckling state, including the wavelength and deformation level. Additionally, we explore how the bandgap can be fine-tuned by altering the material properties and geometric design of the soft laminates.</p>