We establish the state equations for doubly curved, orthotropic shells in an orthogonal Cartesian coordinate system. Modeling orthotropic and anisotropic doubly curved shells in two dimensions, the Carrera Unified Formulation (CUF) technique uses an eight-noded quadrilateral element (Q8) to integrate higher-order shear deformation. The paper uses the Finite Element Method (FEM) to investigate vibration analysis of laminated composite doubly curved shells while accounting for various curvature radii, edge constraints, and six distinct kinds of boundary conditions. Different lamination forms, including two-layer, three-layer, cross-ply laminates (CP), and angle–ply laminates (AP) configurations with symmetric and antisymmetric lamination arrangements, are selected. A unified numerical solution is provided for thin and moderately thick laminated shells. An equivalent single layer with Taylor series expansion is utilized to characterize the displacement field to consider laminated shells. The use of the methodology yields insights into the structural behavior and design issues for doubly curved shells under various scenarios and configurations. Numerical findings are provided for comparison with solutions from the literature to assist designers in determining whether to consider the effects of transverse deformations under different circumstances. The CUF approach generates numerical findings, emphasizing its versatility for diverse laminated composite doubly curved shells.