Dielectric polymers are emerging electro-active materials used in high performance applications such as micropumps, robots and artificial muscles. The development of such applications requires the use of models taking into account the electrical parameters of the material. However, there is still some controversy over the dielectric constant of the most widely used dielectric polymer (VHB 4910, 3M, USA). In this paper, we present an exhaustive study relating to changes in the dielectric constant of VHB 4910 over wide frequency and temperature ranges. We found that the permittivity was a function of: frequency, temperature, the nature of the electrodes and the pre-stress applied to material. Mechanisms of dielectric polarization (β-relaxation) explain the behaviour in temperature and frequency of this parameter. The use of silver grease-compliant electrodes induces an increase in the dielectric constant which moves to a value of 5.4 (against 4.7 with gold electrodes). A pre-strain applied to the material shows a reduction up to 15% in the value of the dielectric constant. Short-range dipolar relaxation, local mechanical constraints in the material and a possible crystallization of material induced by the stretching are suggested to explain these behaviours. Analytic equations of the dielectric constant according to the temperature and pre-strain are then proposed and used to validate the behaviour of these materials for actuator and scavenger devices.