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And Bulldogs captain Steve Price is in danger of missing his side's sudden-death semifinal against Melbourne on Sunday after also being charged.
Finch was slapped with a grade two offence following a 15th minute incident involving Canberra fullback Clinton Schifcofske at Aussie Stadium on Sunday.
The Roosters No.7 would be suspended for two weeks if he entered an early guilty plea and three weeks if he contested the charge at the judiciary and lost.
That would mean the end of his finals series, with the Roosters only one game away from their third consecutive grand final.
If he gets a two-match suspension he would serve out the final week of his ban for the grand final.
Price was charged with grade one striking after an altercation with North Queensland's Glenn Morrison during the second half of Saturday night's qualifying final at Telstra Stadium.
The Queensland prop could miss one game, ruling him out of the semifinal against Melbourne at Telstra Stadium.
Croker was hit with a grade three offence, which could result in a five-match ban, and Smith with a grade two offence.
Kiwi international Smith was also charged with knee lifting following a clash with Crocker in the 18th minute of the game.
He could be banned for a total of seven weeks on the two charges.