<p>Soft dielectric phononic crystals (PCs) offer a promising platform for real-time modulation of elastic wave propagation through external electro-mechanical stimuli. In this work, antiplane wave propagation in two-dimensional soft dielectric PCs is investigated, where periodically distributed soft dielectric tubes are embedded in an elastic matrix and subjected to inhomogeneous electro-mechanical biasing fields. By combining nonlinear electro-elasticity with incremental field theory, the governing equations for antiplane wave dynamics superposed on finitely deformed configurations are derived. To account for spatially varying material properties induced by inhomogeneous biasing fields, a modified plane wave expansion method is developed, and an improved version, based on Laurent’s inverse rule, is further proposed to enhance convergence. The analytical predictions are validated by finite element simulations, showing excellent agreement in both band structures and transmission characteristics. Numerical results reveal that inhomogeneous biasing fields enable effective and reversible tuning of band-gap characteristics, including band-gap opening and closure. Furthermore, the snap-through transition inherent in Gent-type soft dielectrics is shown to induce abrupt variations in band-gap widths, leading to pronounced wave-tunability effects. These findings provide a rigorous theoretical foundation for the design of actively tunable wave devices with applications in vibration isolation, noise mitigation, and acoustic switching.</p>