When the voltage is high enough, compressive hoop stress can induce wrinkles in the annular DE film as shown in our experiments (Fig. 1). By solving the eigenvalue problem formulated in Sec. 3, we can calculate the critical voltage for the onset of wrinkles with different wavelengths in the DE film for different values of *A*/*B*. Our calculation results are plotted in Fig. 6. For a given value of *A*/*B* and wavenumber *k* of wrinkles, the voltage for the onset of wrinkles decreases with decreasing the thickness of the film, namely, *H*/*B*. The results suggest that lower voltage is needed to trigger wrinkle formation in thinner DE films. For different values of *A*/*B*, the wrinkling mode which needs the lowest critical voltage is also different. For instance, in Fig. 6(a), for *A/B* = 0.1, the wrinkling mode with *k* = 2 needs the lowest voltage; in Fig. 6(b), for *A*/*B* = 0.3, the critical mode is *k* = 3. Figures 6(c) and 6(d) show that the critical modes are *k* = 4 and *k* = 6 or 7 for *A*/*B* = 0.5 and 0.7, respectively. In Figs. 6(a)–6(d), we also plot the voltage for inducing pull-in instability in the DE film. For a thick DE film, the critical voltage for wrinkling may be even larger than the critical voltage for pull-in instability. Therefore, for thick DE films, the wrinkles form after pull-in instability, which can be consequently regarded as an indication of material failure.