The stability of arch and shell structures with random imperfections subjected to random loading is investigated. Arches are analyzed under different types of transverse loads while axial and/or pressure loading are considered for cylindrical shells. A probabilistic analysis of the randomness in the geometric imperfections along with the uncertainty in both loading and material properties is presented. The study investigates the effect of spatial variability of the different random parameters in the problem on the buckling load and the associated displacements. The imperfection sensitivity is studied for several geometrical configurations of the arches and shells and for various values of the statistical parameters for the random shape imperfections. One- and two-dimensional random fields are introduced with different types of autocorrelation functions to characterize the structures and the imperfections. A sufficient number of terms is considered using two series expansion methods to express the field in terms of its spectral decomposition. The first employs the Karhunen-Loeve theorem where the autocorrelation coefficient function is expanded in terms of its eigenvalues and eigenfunctions, while the second method utilizes any complete set of orthogonal functions. These techniques are compared with both the midpoint and local averaging methods for random field discretization and prove to be more computationally efficient within a given level of accuracy. Both first- and second-order reliability methods (FORM/SORM) along with Monte Carlo simulation are used to evaluate different modes of instability based on the buckling load or the associated displacements. The probability density and the cumulative distribution functions of the buckling load are presented for various distributions of the imperfections. The sensitivity of the buckling load and the postbuckling displacements to different parameters is also presented. An extensive parametric study through many numerical examples is performed to establish a better understanding of the effects of the spatially variable imperfections on the buckling of arches and shells.