An automatically adjusting seismic restraint system for nuclear fuel storage in one embodiment comprises a free-standing first fuel storage component (FSC) configured to contain nuclear fuel, and a stationary second FSC configured to receive the first fuel storage component. An inter-body gap formed between the FSCs includes at least one seismic restraint assembly. The assembly includes a stationary wedge member fixedly coupled to the second FSC and a movable loose wedge member engaged with and supported in place by the stationary wedge member. The stationary wedge member defines an inclined load bearing surface slideably engaged with a mating inclined load bearing surface of the loose wedge member. During a seismic event or thermal expansion of the first FSC, the first FSC moves towards the second FSC which shrinks the inter-body gap and the loose wedge member is vertically displaced relative to the stationary wedge member while maintaining engagement therewith.