A finite deformation Simo-Reissner peridynamics (PD) shell theory is developed to investigate wave propagation and crack growth in shell structures. Simo-Reissner deformation approximation is utilized to derive the governing equations of the proposed theory from the three-dimensional PD equation. Deformation states for the PD shell theory are identified from the reduced stress power equation. Classical shell constitutive equations are seamlessly incorporated in PD framework by constitutive correspondence approach where a particular form of the classical reduced stress power expression suitable for constitutive correspondence is used. Rotation tensor is updated using an exponential map. A new bond breaking criterion is proposed for PD shell based on critical stretch and critical relative rotation. The solutions of the PD shell governing equations for quasi-static and dynamic cases are obtained through the Newton-Raphson method and the Newmark-beta method, respectively. Numerical simulations include finite deformation of cylindrical shell under both quasi-static and dynamic loading conditions. The PD shell model is validated against finite element solutions obtained using ANSYS®. Crack propagation through the cylindrical shell is simulated under quasi-static and dynamic loading. Wave propagation through cylindrical shell embedded with periodically arranged holes and cracks is investigated. Significant wave attenuation and large bandgap demonstrates the efficacy of the present proposal.