Abstract: A clear understanding of the characteristics and distribution of the process-induced stresses is of importance in improving both the design and the fabrication process of composite wound structures. For predicting the distributions and magnitude of such stresses, many investigators have proposed some finite element models based on minimized potential energy principal. However the continuity conditions of the inter-laminar stress field of neighboring layers along the interface can not be satisfied accurately for those models, an efficient finite element method based on rigorous elasticity theory is needed. In the present study, an analysis of the process-induced stress was conducted on the basis of a systematic Hamiltonian thermo-elasticity theory in conjunction with semi-analytical finite element method. The set of first order ordinary differential vector equations were solved by the precise integration method. From numerical results for a typical example of process-induced stress analysis of a composite wound vessel with a metal liner, it is clear that the process-induced thermo-stress fields involve complex variations of gradient and multi-peak values at different stages during the curing process. This is the reason for pre-failure damage of such composite winding layers, which results in a reduction of their load carrying capacity. The method and numerical conclusions provided in this paper should be of great value to engineers dealing with composite wound structures.