Various constitutive formulations can be employed to simulate the coupled behaviour of electro-active polymers (EAP). Those distinct mathematical descriptions vary with respect to the manner in which the electric field is coupled to the deformation. However, in principle, they are all capable of emulating the finite coupled response of EAP. The underlying coupling mechanism of largely deformable materials can be identified through experimental characterization. This contribution addresses the constitutive and finite element modelling of the actuation response of both isotropic and anisotropic EAP, where different material formulations are considered and implemented within a finite element framework. Those various material formulations are mathematically treated and employed to simulate electro-mechanical experiments of dielectric materials. Existing coupled electro-mechanical tests of active materials are referred to, where it is sought to employ different constitutive models to fit the experimental observations. Within the undertaken study, the capability of different descriptions to predict electro-mechanical instabilities is evaluated. Regarding the numerical implementation of the model, it is referred to an electro-mechanical Q1P0 finite element formulation. After performing the study and fitting experimental results associated to isotropic materials, the actuation response of several anisotropic EAP-based structures is emulated.