In this study, the nonlinear axisymmetric behavior of circular isotropic plates with linearly varying thickness under random excitation is investigated. It is assumed that plate response is axisymmetric when plate is subjected to axisymmetric random loading. The Berger type nonlinearity is used to obtain the governing equations of motion for clamped circular plates. A Monte Carlo simulation of stationary random processes, single-mode Galerkin-like approach, and numerical integration procedures are used to develop nonlinear response solutions. Response time histories, root mean squares and spectral densities are presented for different random pressure levels. Parametric results are also presented. Linear responses are included to investigate the nonlinear effects.