•A 3-D damage plasticity based FE model is developed for SCS sandwich shells.•Geometry and material nonlinearities were considered in the FE model.•The influence of the curvature on the resistance of SCS sandwich shells was studied.•The accuracy of analytical models on the resistance of sandwich shells was checked. This paper develops a three-dimensional damage plasticity based finite element model (FEM) to study the ultimate strength of the steel–concrete–steel (SCS) sandwich shell structure under patch loading. The FEM considers complex geometric nonlinearities of hundreds of stud connectors in the structure, complex interaction between the connectors and concrete, and material nonlinearities of steel and concrete used in the structure. In the developed FEM, the concrete core material adopts the concrete damage plasticity model to predict the post-peak softening and residual strength; the stud connectors and steel shells adopt a continuum damage model to phenomenologically describe the damage evolution in the steel material. The reasonable agreement between FE analysis and the quasi-static tests on the SCS sandwich shell structure confirms the accuracy of the FEM in predicting the ultimate shear resistance, load–deflection relationship, cracks in the concrete core, and punching shear failure of the top steel shell. A subsequence parametric study based on the validated FEM investigates the influence of the curvature on the first peak resistance of the SCS sandwich structure. Finally, the paper validates accuracy of an analytical model on the punching shear resistance of the concrete core of the SCS sandwich shell.