In this work, we introduce a novel 3D exact model for the analysis of the transient mechanical behavior of laminated composite plates and shells. The system of equations obtained by using Hamilton’s principle, and the generalized ABCDE-matrix that accounts several essential mechanical couplings (due to variation in the thickness and section warping) often neglected in the classical literature. The stretching-throughthe-thickness term is rigorously justified by the existence of potential of distortion proved here. It’s found important to develop rigorously 3D exact analysis of mechanical behavior to improve the quality and resistance of laminated plate and shell structures for variety of applications. The proposed equations are assessed to show the performance of some matrix systems developed here in some selected test cases found in the literature. The 3D exact analysis proposed in the current work, improves many recent studies on the analysis of laminated composite plates and shells. Moreover, the generalized ABCDE-matrix has a great potential to increase the predicting power of the mechanical behavior of civil structures and the accuracy of analysis meanwhile reducing the computational costs.