Hello, my 427 is backfiring when I give it gas from 2 to 3 and 4th.  Even cruising in 4th, I give it more gas and instantly backfires.  It idles perfectly, not missing.  I check the spark plug wires and all are functioning correctly.  Could it be the vacuum system? 

what type of dist ,did u just take it out of storage?,could be water in gas a clogged fil,ter, bad coi,l or cond ,really need more info what year 427, hp ,stock orig or something else,mike

"Backfiring"....thru the exhaust, or thru the carb? 

If thru the carb, I would first suspect a carb problem, such as the accelerator pump not working properly.

Late ignition timing could do that too, as well as cross-firing plug wires, a bad distributor cap/rotor, or worn points.