Dielectric elastomers are widely investigated for use as actuators, stretch/force sensors and mechanical energy harvesters. As performance of such devices is limited by the elastomer’s dielectric strength, it is important to investigate the factors that mostly affect the electrical breakdown of those materials. In this paper, we present a preliminary study on the breakdown strength of a widely used poly-acrylic elastomer film, VHB 4905 by 3M with an equi-biaxial pre-strain of 300%. The breakdown was measured with two metal electrodes, one hemispherical and the other one planar, and was characterized under different conditions to investigate the effects of the hemispherical electrode’s curvature, the force applied by the two electrodes and the environmental humidity. With a given radius of curvature, the breakdown field increased by about 50% for a nearly ten-fold increase of the applied mechanical force, while, for a given mechanical force, the field decreased by about 20% for a two-fold increase of the radius of curvature. Furthermore, for a given radius of curvature, an increase of the environmental relative humidity from 0% to 80% caused a reduction of the breakdown field of about 20%. This study shows that the breakdown field of the studied dielectric elastomer is highly dependent on the boundary conditions of the breakdown test, as well as the environmental/storage conditions of the material. Therefore, such conditions must be reported carefully to allow for critical evaluations/comparisons of experimental results. As suggested by our data, variations of the compression, electrode’s curvature and environmental humidity are likely to cause a diversity of possible interplaying effects, some of which are preliminary proposed in this paper and are referred to as topics requiring deeper future investigations.