The main problem to obtain considerable deformation with dielectric electro-active polymer based technology is the electrical breakdown. A simple solution consists in pre-stretching the elastomer before activating it which cancels the snap-through effect and thus avoid reaching the electrical limit. Due to the stress characteristic of the DEAP, it could be demonstrated that a spring with a negative stiffness provides the best strain. In this paper, a new design of a monostable spring with a negative stiffness is suggested for a DEAP tubular shape actuator. The particularity of the proposed solution is the radial direction of the displacement with a special load characteristic. In order to determine the performance of the system, the mechanical and electrical behaviour are investigated through analytical models with the assumption that the axial stretch stays constant. A finite element method is used to validate these latter and maximal error lower than 2% is reported. The energy chain conversion is developed in detail which allows studying all the energies transferred from both the electrical input and any pre-stretch solution to the membrane during a cycle of activation. From these models, the negative stiffness spring is compared to the common solution, i.e a constant pressure or a linear positive spring, to pre-stretch a cylindrical EAP. The results show that the linear spring always removes the snap-through behaviour contrary to the constant pressure. Depending on the geometry, the monostable solution cancels also this latter and owns a better energy transfer from the power supply to the elastomer (around 50% against 40% for the linear spring) or a better stroke compared to the linear spring. Furthermore, due to the hollow in its stress characteristic, the cylindrical shaped actuator associated to a linear spring or the proposed spring allows increasing the strain. Through the different analytical models, the definition of the electrical breakdown and the analysis of the limits of the stresses, a qualitative study of the performance is given for the different pre-stretches.