A finite element formulated on the basis of the layerwise linear displacement theory is used to study the first-ply failure of moderately thick laminated composite plates. In the finite element formulation, a laminated composite element is divided into a number of mathematical layer groups and displacements are assumed to vary linearly in each layer group which contains eight nodal points. The accuracy of the finite element in predicting displacements and stresses has been verified by comparing results with experimental data and previously obtained analytical results. The finite element is used to determine the first-ply failure loads of a number of laminated composite plates on the basis of several phenomenological failure criteria. The capabilities of the failure criteria in predicting first-ply failure loads are investigated by comparing the finite element first-ply failure loads with the experimental ones. It has been found that the failure criteria can yield reasonably good results for the cases considered.