The recent discovery of electro-active polymers has shown great promises in the field of soft robotics, and was logically followed by experimental, numerical and theoretical developments. Most of these studies were concerned with systems entirely covered by electrodes. However, there is a growing interest for partially active polymers, in which the electrode covers only one part of the membrane. Indeed, such actuation can trigger buckling instabilities and so represents a route toward the control of 3D shapes. Here, we study theoretically the behaviour of such partially active electro-active polymer. We address two problems: (i) the electrostatic elastica including geometric non-linearities and partially electro-active strip using a variational approach. We propose a new interpretation of the equations of deformation, by drawing analogies with biological growth, in which the effect of the electric voltage is seen as a change in the reference stress-free state. (ii) we explain the nature of the distribution of electrostatic forces on this simple system, which is not trivial. In particular we find that edge effects are playing a major role in this problem. Soft robotics is a new, rapidly developing scientific field. It aims at designing compliant robots able to move in topographically complex environments or able to manipulate fragile objects [1-3]. Potential applications range from artificial heart [4] to bio-inspired loco-motion [5, 6] or haptic interfaces for virtual reality where the user feels a feedback force from the interface that he manipulates[7]. Electro-Active Polymers offer a promising candidate for building such soft robots. Their large reversible deformations (tens of percent strains) under an applied electric field, triggered a huge interest in academic laboratories over the world [8]. Several types of electro-responsive polymers have been described in the literature , such as anionic, ferroelectrics, liquid-crystalline, electro-rheological [9-11]. In this paper, we are specifically interested in Electro-Active-Polymers (EAP), which are the most simple and inexpensive in terms of manufacturing [12]. In their simplest form, EAP are indeed composed of a thin membrane of elastomer covered by two conductive compliant layers. When an electric field is applied, the electrodes of this soft capacitor are attracted to each other, resulting into in-plane isotropic strain. A wide range of applications of EAPs have been proposed, they include: robots actuation [13-16] , rotational motors [17], flapping wings [18, 19], valves [20, 21], actuators for biological cells [22], Braille displays [7, 23, 24], tun-able lenses ([25], [26]), artificial chromatophores [27, 28], tunable diffracting surfaces [29] or phase shifters for microwave communications [30]. As in the case of piezo-electric ceramics, this electro-mechanical coupling can potentially be reversed in EAPs: an electric power may be harvested from mechanical strain [31-34], or conversely , the device may work as a mechanical sensor [35, 36]. In this article we investigate theoretically the behaviour of an electro-active polymer in the case where its surfaces are not entirely covered by conductive electrodes. This situation is interesting as it leads to buckling instabilities and is a way to obtain out-of-plane shapes [37-39] through the non-linear response of the structure. The aim of this article is to clarify three questions that arise in this problem. Namely, the literature usually considers membranes completely covered by conductive electrode, and one usually models electrostatic effects by an electrostatic pressure which is twice the actual value of the pressure [8], in the case of incompress-ible elastomers (ν = 1/2). In this article we will refer to this description as "Pelrine's approach". The argument is based on the superposition of an isotropic stress (which has no effect on an incompressible material) to the actual electrostatic pressure on the faces [40]. The questions we would like to address are: (i) Does this argument apply to cases where electrostatics is only active on a portion of the plate? (ii) Does the argument remain valid for non-planar buckled states? (iii) Can we determine the real distribution of electrostatic forces and relate it to the electromechanical equilibrium of a strip? Indeed standard approaches [40, 41] provide a calculation of the mechanical stresses in the material resulting from the electrostatic loading, and even to adequately predict the onset of wrinkling and its possible evolution in pull-in instability [42], but do not provide the real distribution of electrostatic forces from which they originate. In this article we use a variational approach to clarify the nature of electrostatic forces acting on an elec-troactive membrane. Our aim is to make an explicit link between variational and stress-based approaches of