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[burger and fries]

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[shellslinger]

Perhaps older non-modern barrels it will cause damage. But as I recall, with most modern shotguns, steel shot is fine.

[Barbarossa]

Do the dime test.(rule of thumb)

If a dime will pass through the end of the barrel it is open enough to shoot steel, providing the steel of the barrel is of sufficient strength/quality.

[mjsweims]

Shotguns built from the sixties on are fine. Before the 50s you should not use steel shot.
Guns built in the 50s are a toss up - sometimes they will say safe for steel other times nothing. If the gun maker is still around you can check with them. If in doubt don't use steel.