The linear static elastic-plastic behavior of sandwich cylindrical shell panels under a generally distributed loading with thick flexible core is studied. The core modeling is based on high-order theory of sandwich structures in which the in-plane stresses of the core are neglected. The faces are modeled based on Kirchhoff–Love shell theory. The materials of the faces and the core are assumed to be isotropic with linear work hardening behavior. The incremental Prandtl–Reuss plastic flow theory is used in this analysis. Using the principle of virtual displacements, the governing equations are derived and solved for any sort of boundary conditions based on elastic-plastic harmonic differential quadrature method. To validate the results of present study, various responses in different sandwich shell panel configurations are compared with the results from finite element software Ansys. The effect of core flexibility and its plastic properties as well as the initiation of yield in faces and the core are studied in detail.