By calculating the transmission coefficients by finite-element software, the study of thetunable acoustic band gap for two-dimensional (2D) phononic crystals composedof a square array of hollow cylinders in an air background is considered. Theinclusions are a dielectric elastomer cylindrical actuator, which is made of a hollowcylinder sandwiched between two compliant electrodes. By applying a voltagebetween the compliant electrodes, the radial strain of the silicone-made actuator isinvestigated. The acoustic band gaps are changed due to the radial strain of thedielectric elastomer. The frequency range of the dielectric elastomer composite canbe extended by increasing the applied voltage. A tunable acoustic band gap ofthe phononic crystal is realized via the unique character of dielectric elastomer.The calculations also demonstrate that there exists a local stop band within the pass band.With a local stop band gap, 2D phononic crystals may thus serve as an acoustic filter orswitch.