Offshore structures are exposed to the risk of damage caused by various types of extreme and accidental events, such as fire, explosion, collision, and dropped objects. These events cause structural damage in the impact area, including yielding of materials, local buckling, and in some cases local failure and penetration. The structural response of an FPSO hull subjected to events involving dropped objects is investigated in this study, and non-linear finite element analyses are carried out using an explicit dynamic code written LS-DYNA software. The scenarios involving dropped objects are based on the impact from the fall of a container and rigid mechanical equipment. Impact analyses of the dropped objects demonstrated that even though some structural members were permanently deformed by drop loads, no failure took place in accordance with the plastic strain criteria, as per NORSOK standards. The findings and insights derived from the present study may be informative in the safe design of floating offshore structures.