Beretta.net

I am wondering if I could use a 1 ton engine hoist to lift the engine out of my 1989 Chevy Beretta base

Yes, one ton equals 2000 pounds. A Beretta engine is roughly less than a quarter of that total.

I always found that lifting the body off the engine/trans and subframe was easier... Just set some jacks stands under the subframe, disconnect the battery, all hoses, electrical connections (mark what they go to!), shift linkage, and fuel lines then unbolt the struts and calipers from the knuckles. Now unbolt the 12 subframe bolts and lift the front of the car up (I've had good experiences by using a chain or lifting strap between the front bumper shocks and an engine hoist) and roll it back. Now you've got lots of room to clean things up and make the swap as easy as pie.

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Oh look another new guy with an 89 Base
Anyways yeah I think no matter the engine you got in there it should be able to pull it. Just follow Jeff's advice.