The blast resistance of a sandwich-walled cylinder/ring comprising two metal face-sheets and a graded metal foam core, subjected to internal air blast loading, is investigated. Analytical models are developed for the deformation of the sandwich cylinder with positive and negative gradient cores under internal blast loading. The deformation process is divided into three distinct phases, namely the fluid–structure interaction phase, core-crushing phase, and outer face-sheet deformation phase. Finite element modeling is performed using the Voronoi material model. The proposed analytical models are verified through finite element analysis, and reasonable agreement is observed between the analytical predictions and finite element results. The sandwich structures with high energy absorption capacity or low maximum radial deflection are satisfied for the protecting purpose of impact/blast resistance requirements. Typical deformation processes are classified and analyzed; the effects of explosive charge, face-sheet thickness, and core gradient on the structural response are also examined. The results indicate that both the deformation modes and the structural response of the cylinders are sensitive to the blast charge and core configuration. It is concluded that energy absorption capacity and maximum radial deflection are two conflicting goals for achieving high impact/blast resistance capability. An in-depth understanding of the behavior in sandwich-walled cylinders under blast impulse and the influence of the core configuration helps realize the advantages and disadvantages of using graded foam materials in sandwich structures and can provide a guideline for structural design.