In this study, the nonlinear response characteristics of electrostrictive material sensors subjected to stochastic excitation were investigated. Van der Pol nonlinear differential items were developed to interpret the hysteretic phenomena of electrostrictive materials. The hysteretic constitutive models of electrostrictive materials were proposed, and the nonlinear dynamic model of electrostrictive material sensors subjected to stochastic excitation was developed. The expression of the dynamic response of the system was obtained, and the bifurcation conditions and chaos characteristics of the system were determined. Finally, the effects of system parameters on the dynamic characteristics of the system were analyzed. The simulation results show that there were bifurcation phenomena in the system, which can be suppressed by adjusting the parameters. The stochastic noise intensity had an important effect on the system dynamical response, and the stochastic resonance phenomenon occured with the variation in stochastic noise intensity. The results of this study were helpful for the optimal design and improvement of electrostrictive material sensors.