A novel concept of steel–concrete–steel (SCS) sandwich conical structure has been developed for the Arctic offshore platforms. In this structure, punching shear resistance to localized patch loading is the main concern that considers the high pressure zones due to nonuniform distribution of the ice contact pressure. In this paper, quasi-static tests on nine large scale SCS sandwich shell structure were firstly carried out to investigate the ultimate strength behavior of the SCS sandwich shell structure under patch loading. Based on these test results, the influences of different parameters on the ultimate resistance were discussed and analyzed. These studied parameters are composite action, steel shell thickness, spacing of connector, strength of concrete core, and curvature of the sandwich shell. Theoretical models were developed to predict the shear resistance of the SCS sandwich shell structure. The innovations of the developed models include developing formulae to predict the resistances of the connector used in the sandwich shell structure, redefining the critical perimeter to analyze the punching shear resistance of SCS sandwich shell, and modifying the formulae in Eurocode 2 to calculate the punching shear resistance. The accuracy of the developed prediction models were checked and confirmed by nine reported tests and 11 tests in the literature. Finally, design recommendations on the punching shear resistance of the SCS sandwich shell were offered based on the discussions and validations.