Abstract: Vessel structural support system for laterally and vertically supporting a vessel, such as a nuclear steam generator having an exterior bottom surface and a side surface thereon. The system includes a bracket connected to the bottom surface. A support column is pivotally connected to the bracket for vertically supporting the steam generator. The system also includes a base pad assembly connected pivotally to the support column for supporting the support column and the steam generator. The base pad assembly, which is capable of being brought to a level position by turning leveling nuts, is anchored to a floor. The system further includes a male key member attached to the side surface of the steam generator and a female stop member attached to an adjacent wall. The male key member and the female stop member coact to laterally support the steam generator.