A higher-order Equivalent Layer-Wise (ELW) theory is formulated for the multifield analysis of fully anisotropic laminated doubly-curved shell structures of arbitrary geometry under thermodynamic equilibrium conditions [1]. The model accounts for the full coupling among mechanical elasticity, electrostatic, magnetostatic, and hygro-thermal fields, thereby enabling the systematic inclusion of multiple interacting physical phenomena [2]. The governing equations are derived within a unified formulation for the kinematic expansion of the unknown field variables and are obtained from the Master Balance Principle expressed in principal coordinates [3]. An isogeometric mapping of the physical domain is employed to accurately represent shell structures of arbitrary shape. The numerical implementation is conducted within the Finite Element Method (FEM) framework, adopting Lagrange and Hermite interpolation functions, which allow the efficient treatment of bi-connected domains characterized by geometric discontinuities and internal cut-outs [4]. In addition, an analytical homogenization procedure based on the Mori–Tanaka scheme is introduced to evaluate the fully coupled effective constitutive properties of the laminae. In the post-processing, a patch-based recovery procedure, combining Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ), is used to recover the primary and secondary multifield variables. A comprehensive numerical campaign is presented to assess the static multifield response of laminated shell structures with varying curvature radii and stacking sequences. The numerical results are validated through systematic comparisons with three-dimensional finite element simulations obtained using commercial software, as well as with available semi-analytical Navier-type solutions. Parametric studies are further carried out to quantify the influence of the various physical couplings on the structural response. The proposed framework provides a robust, accurate, and computationally efficient methodology for the analysis and design of complicated shell structures under multiple physical fields.