In the present study, the shock-absorbing behavior of cork-based sandwich structures was investigated. Three different facesheets, made from AFRP, CFRP, and GFRP, were used in the sandwich structures. An agglomerated cork with a thickness of 10 mm was used as the core material in the sandwich structures. Shock-absorbing tests were carried out using a drop tower system by dropping a hemispherical impactor onto the specimens. A load cell was used to collect the backface forces during the impact processes. According to the results, the CFRP-based sandwich structure had the lowest reaction force, although the other specimens showed quite similar results. On the other hand, the AFRP-based specimen had the longest shock-absorbing duration among the specimens investigated in this study. The core material is the main shock-absorbing component in sandwich structures, while facesheets contribute minimally to the shock-absorbing process. However, facesheets play an important role in distributing the impact loads over a larger area on the core material, consequently enhancing the shock-absorbing capabilities of the sandwich structures. Cork, as a core material in sandwich structures, exhibits excellent shock-absorbing properties due to its cellular microstructure.