A non-ordinary state based peridynamics (PD) shell piezoelectricity formulation is presented. The deformation field and electric potential field are assumed to vary linearly with the coordinate along the thickness direction using Taylor series expansion and retaining the first-order term. Neglecting drilling rotation, this introduces a total of seven degrees of freedom at any point in the shell. Governing equations of both classical and PD shell piezoelectricity are derived by employing Hamilton’s principle, using the proposed assumptions on deformation and electric potential fields, and integrating the thickness coordinate out. Classical piezoelectric shell constitutive equations are derived from the three-dimensional constitutive equations of piezoelectricity. The deformation states associated with the classical and PD shell theories are systematically identified from the reduced stress power equation. Classical shell constitutive equations are incorporated into the PD framework using the constitutive correspondence approach, where an equivalence of internal virtual work from classical and PD shell theories is used. PD shell governing equations are linearized, and the Newton–Raphson method is employed to obtain solution under quasistatic loading. Newmark-beta method is used for the dynamic case. Numerical simulations are conducted for a solid cylindrical shell, a shell with a hole and shell metasurfaces under various loading and boundary conditions, and the results are validated against finite element solutions obtained using ABAQUS®. Crack propagation in piezoelectric shell structures is further investigated under displacement-controlled quasi-static loading. Dynamic simulations encompass wave propagation in solid piezoelectric shell structures and metasurfaces, as well as crack propagation in pre-cracked piezo-shells, thereby demonstrating the fidelity of the proposed approach.