Dielectric elastomer actuators (DEA) have been demonstrated to exhibit a quasi-immediate electro-mechanical actuationresponse with relatively large deformation capability. The properties of DEA make them suitable to be used in the form ofmajor active components within soft robotics and biomimetic artificial muscles. However, some of the electro-active materialproperties impose limitations on its applications. Therefore, researchers attempt to modify the structure of the homogeneousDEA material by the incorporation of fillers that possess distinct electro-mechanical properties. This modification of thematerial’s structure leads to a fabricated inhomogeneous composite. From the point of mathematical material modelling andnumerical simulation, we propose a material model and a computational framework using the finite element method, whichis capable of emulating nonlinear electro-elastic interactions. We consider a coupled electro-mechanical description withthe electric and the electro-mechanical properties of the material assumed to be nonlinearly dependent on the deformation.Furthermore, we demonstrate a coupled ansatz that expresses the electric response as dielectrically quasi-linear with onlydensity-dependent electric permittivity. We couple the electro-mechanical models to the extended tube model, which is asuitable approach for the realistic emulation of the hyperelastic response of rubber-like materials. Thereafter, we demonstrateanalytical and numerical solutions of a homogeneous electro-elastic body with the Neo-Hookean material model and theextended tube model to express the hyperelastic response. Finally, we use the finite element method to investigate severalheterogeneous configurations consisting of soft DEA matrix filled with spherical stiff inclusions with changing volumefraction and ellipsoidal inclusions with varying aspect ratio.