Electro-active polymers (EAP) are smart materials that can deform dramatically and quasi-instantaneously in response to anapplied electric field. These properties make them suitable to be used as soft robotic actuators. As any passive rubber-likematerial, those electro-sensitive components are quasi-incompressibleand may show pronounced time-dependent hysteresisbehaviour. The direction of the electric field induced deformation can be tuned by incorporating stiff fibres in a relativelysoft EAP, which renders an anisotropic mechanical response of the whole composite. The contribution at hand presents aconstitutive model which is suitable for the simulation of an electro-viscoelastic behaviour of transversely isotropic EAP. Thematerial model is based on an additive split of the total energy function intopurely mechanical, electrical and coupled electro-mechanical contributions. The mechanical part of the energy is further decomposed into isotropic and anisotropic parts. Forthe electrical and the coupled contributions, formulations for both the perfectly linear dielectric and the nonlinear (deformationdependent) electrical response are presented. Regarding the numerical implementation, a mixed quasi-incompressible andquasi-inextensible electro-mechanical finite element is developed. In addition to the displacement and electric potential, fouradditional field variables are introduced. The capabilities of the proposedtheory and its numerical treatment are demonstratedthrough simulations of several electro-mechanical actuator structures. The utilization of a quasi-inextensible finite elementis shown to improve the convergence behaviour of the numerical solution, allowing for the simulation of complex loadingscenarios of fibre reinforced EAP in an efficient manner.