Abstract: The strength of a thick-walled vessel with alternate-ply filament winding(FW) outside an isotropic liner under internal and external pressure was investigated by three-dimensional (3D) orthotropic stress-strain relation and axisymmetric thick-walled cylinder theory. The stresses of the liner and the fiber layer, as well as longitudinal stress along the fiber direction, transverse stresses perpendicular to the fiber direction and shear stress were obtained analytically. Using Hoffman failure criteria and Tsai-Wu 3D failure criteria, the strength of the filament layer of FW cylinder with respect to thickness and winding angle was investigated by the thin-walled theory and 3D theory, respectively. The strength of FW vessel with a liner with respect to winding angle was compared numerically with FW vessel without a liner. Numeric results of finite element (FE) model were presented in ANSYS software by layered element SOLID191, and perfect agreement of stresses in fiber directions and strength ratio between FEA and the theory was achieved. It is found that the laminate theory gives imprecise two dimensional fiber stresses, in which transverse stresses lead to lower strength estimation. The influence of the thickness-radius ratio to strength ratio is different for different filament types and winding angles, and the strength ratio given by 3D stress analysis under external pressure is far beyond the thin-walled theory. The comparison shows that the strength ratio of FW vessel without a liner is more sensitive to winding angle than the vessel with a liner.