Composite sandwich structures are widely used in many areas. Light materials, such as honeycomb panels, are usually used as the cores, while stiff materials, such as fiber reinforced polymer laminates, are used as the facesheets. In this work, corrugated cores for sandwich structures were fabricated using carbon fiber reinforced polymers (CFRPs) featuring different stacking orientations. Paper, aluminum, and polypropylene honeycomb cores were also used. Additionally, CFRP was utilized as the facesheets for these sandwich structures. Bending tests, face-wise compression tests (FCT), edgewise compression tests (ECT), and accelerated aging were conducted. Finite element simulations were also performed and compared with experimental results. The results indicated that the corrugated CFRP cores with [0°]5 stacking orientation resulted in the largest flexural stiffness and ECT strength along the flute direction. Conversely, the corrugated cores with [90°]5 stacking orientation resulted in the largest transverse shear rigidity and modulus, FCT modulus and strength, and ECT strength perpendicular to the flute direction. Notably, the sandwich structures using aluminum honeycomb cores were degraded by aging the least. Since sandwich structures can be subjected to the bending load and loads in other directions, this work contributes to selecting core materials and structures of sandwich structures.