There is an important difference between piezoelectric polymer films and solid crystals for the application of piezoelectric generators. In the case of polymers, the optimal piezoelectric response imposes a large bending regime. Starting from the linear Curie’s constitutive equations, we develop an analytical model under the assumption of the large bending regime resulting from bulge testing configuration. This model shows a specific non-linear piezoelectric response, which follows a power of 2/3 of the mechanical excitation. The piezoelectric voltage and the corresponding power are then studied experimentally as a function of the angular frequency ω of the mechanical excitation, the load resistance R, and the thickness of the film ℓ. The experimental results carried out on piezoelectric polyvinylidene fluoride (PVDF) films validate the model.