I have a 82 Z28 with a 4bbl carb on a stock 350. It started doing it just recently not really sure why. Whenever I accelerate or take off from a stop the car shudders really hard and its really annoying. I thought it was u joints but inspected them and have no play. When you hold the brake and put in drive or reverse you can see the whole engine shudder and idles really rough. I am NOT having any misfires or backfires. I recently replaced the intake gasket due to a bad leak. Its no longer leaking. Really not sure.

 

check your compression, could be a dead cylinder. Could also be running on 7 for other reasons.

 

Sure you got your timing set right? Got all you vacuum stuff reconnected properly? Even though you have no backfires, you may have plug wires crossed.

Do a cranking compression test by disconnecting the BATT wire from the distributor. Then hold the throttle to the floor and crank the engine. Listen for uneven cranking, like one or more low cylinders. If it cranks normal, you have fuel or spark distribution problems, or possibly a stuck open EGR valve. If it cranks uneven, grab the compression gauge and see what's up. You may be able to save time on the compression test if you can isolate the low cylinder with a power balance/cyl drop test.