Purpose <p>This study investigates the buckling and free vibration behavior of skewed doubly curved sandwich shell structures, which are widely used in aerospace, automotive, and marine applications. The aim is to understand how various geometric and material parameters influence the dynamic and stability characteristics of these advanced structures.</p> Methods <p>The sandwich shell under consideration consists of three layers: a viscoelastic core, a functionally graded material (FGM) top skin composed of a ZrO₂/Al ceramic–metal combination, and an isotropic bottom skin. Constrained layer damping is introduced by embedding the viscoelastic core between the top and bottom layers. The analysis is performed using First-Order Shear Deformation Theory (FSDT), and the governing equations of motion are derived through Hamilton’s principle and solved using the Finite Element Method (FEM).</p> Results <p>A comprehensive parametric study is conducted to evaluate the effects of key parameters such as skew angle, core thickness ratio, power-law index of the FGM layer, boundary conditions, core loss factor, constraining layer thickness, and different shell geometries. The results demonstrate significant variations in natural frequencies and buckling loads depending on these parameters, highlighting the critical role of material gradation and structural configuration in the performance of sandwich shells.</p> Conclusion <p>The findings confirm that skew angle and FGM properties notably enhance structural stiffness and dynamic response, while the viscoelastic core contributes to energy dissipation. The study provides valuable insights for the optimal design of sandwich shell structures, and the adopted FSDT-FEM framework offers reliable predictions suitable for engineering applications.</p>