Acceptance and utilization of composite materials require confidence in their load carrying capacity. Therefore, it is desirable to develop a computational model capable of determining the ultimate strength of laminated composite plates under conditions of complex loading. A new seven degree of freedom finite element model for laminated composite plates is developed. The model utilizes three displacements, two rotations of normals about the plate midplane, and two warps of the normals, to accurately and efficiently determine the laminate stresses. Based on these stresses a failure model for determining first ply failure (FPF) and last ply failure (LPF) by a progressive stiffness reduction technique has been developed. The progressive failure model produces results in good agreement with experimental data. The calculated FPF and LPF results form lower and upper bounds within which the true load carrying capacity lies.