Abstract: Most previous investigations on inerter did not consider effects of gap nonlinearity, however, it is demonstrated that the effects of over-large gap on system responses should not be ignored. A stochastic differential equation of inerter-rubber vibration isolator with gap nonlinearity is established in this paper, the statistical moments of system responses are derived by the stochastic nonlinear analysis method, and the probability density function is further obtained. The failure probabilities are obtained by reliability analysis, and the effects of gap on system response are analyzed. Moreover, effects of gap nonlinearity under nonstationary excitation on system responses and reliability are also considered. Results show that when the gap value increases, the statistical moment of the system response increases, the probability density function curve becomes flat, and the failure probability of the system increases rapidly, which are different from those of deterministic analysis; therefore, it is advised that the effect of gap on dynamic reliability of system should be considered in the design of vibration isolator.