This paper develops a finite deformation Simo-Reissner geometrically exact shell theory in both classical continuum mechanics and peridynamic (PD) frameworks that can capture warping deformation. At each material point, seven degrees of freedom are considered, viz., three translations, two in-plane incremental rotations, and two warping amplitudes. In this model, the straight fibers along the thickness direction before deformation do not remain straight after deformation but become curves due to warping. A kinematic assumption on the deformation field is proposed. The governing equations of both classical and PD warping-enabled shell models are derived using Hamilton’s principle, the proposed kinematic assumption, and through-the-thickness integration. The elastic constitutive relations for classical shell warping model are derived starting from the three-dimensional generalized Hooke’s law using our kinematic assumption and integrating through-the-thickness. Constitutive correspondence method is used to incorporate the classical warping-enabled shell constitutive equations into the PD framework. Numerical implementation strategy is developed for both quasi-static and dynamic problems. The PD governing equations are linearized, and the Newton-Raphson method is employed for quasi-static case. The dynamic PD governing equations are solved using the implicit Newmark-beta method in conjunction with the Newton-Raphson method. Numerical simulations are performed on a solid cylindrical shell, a shell with a single hole, and metasurfaces such as shells with multi-cracks and multi-holes subjected to various loading and boundary conditions. The results demonstrate that the proposed theory is effective in capturing warping-induced deformation in shells.