When subject to an electric field, a dielectric elastomer (DE) deforms, possibly straining over 100%. Due to their distinctive mechanical properties, the DEs are being developed as actuators for broad applications, such as armaria, adaptive optics, and robots. According to a method to study instabilities of DE films proposed by Tommasi et al, this paper focuses on analyzing wrinkling and pull-in instabilities of circular dielectric elastomer actuators in order to guide the design of actuators conveniently and directly. Based on simple geometrical and material assumptions, the authors consider the effects of pre-stretch, the size of activated region and material model, which are all crucial in technological applications of DEs. A valid analytical method is used to describe the occurrence of wrinkling and pull-in, which gives clear physical interpretations of these failure mechanisms. As a result, this paper gives a series of critical parameters corresponding to instabilities in different pre-stretch values and the optimal pre-stretch values for some needs. They agree with the experiments well.