Abstract The initiation and propagation of uncertainties in structural behavior of complex anisotropic sandwich structures have significant computational challenges. Owing to limitations of experimental data, probabilistic descriptions of uncertain parameters are not practically feasible to expedite. This chapter presents the prediction capability of a surrogate model (polynomial neural network [PNN]) to estimate the stochastic buckling behavior of sandwich plates. The PNN is used to construct the surrogate. The computational time and cost is significantly reduced by using the proposed model in conjunction to finite element model using higher order zigzag theory. Both material and geometric uncertainties are considered to obtain the statistical quantity of interest. The computational efficacy of PNN is validated by means of scatter plot and probability density function plot. The constructed PNN model is found to be convergent with the results obtained by direct Monte Carlo simulation techniques. The proposed model can be used for more complex structures in future.