Due to their high strength to weight ratios, laminated composite materials have found extensive applications in the construction of mechanical, aerospace, marine and automotive structures. Predictions of the failure of composite structures and the maximum loads that the structures can withstand have become an important topic of research for reliability assurance. In particular, the first-ply failure analysis of laminated composite plates subjected to transverse loads has drawn close attention in recent years. Accurate prediction of failure of composite structures has become more challenging to designers in the presence of inherent scatter in the material properties. The objective of the present study is to improve the efficacy of composite material design by predicting the statistics of first-ply failure of orthotropic plates with random material properties under random loading. In the present study stochastic finite element solutions of probabilistic failure load of composite laminated plates are obtained with layer-wise plate theory and analytical solutions are found using Kirchhoff-Love plate theory. Tsai-Wu and Hoffman criteria have been adopted to predict the first-ply failure load and first-order perturbation technique has been used to evaluate the mean and variance of failure statistics. The capability of stochastic finite element in predicting the first-ply failure load statistics has been studied by comparing the results with analytical solutions. It has been found that the stochastic finite element has high accuracy for the cases considered. The present solutions are also compared with results available in the literature. Numerical results have been presented to illustrate the application of the developed procedure. © 2005 Elsevier Ltd. All rights reserved.