I have a 302 chevy engine in my 54 Chevy that just shuts off after running for a few minutes why?

fuel line collapse somewhere in line from tank or vent on gas cap not working correctly

I've taken the gas cap off and it still happens. After it shuts off it won't start for a few minutes. After a few minutes it starts right up and runs for a few minutes then shuts off.

What do you have in there for an ignition system? HEI or points.

it's an HEI

I believe it's an HEI, this was my dad's car and after he passed I bought it off my mom to keep it in the family. I don't know a lot about cars but I'm learning.

Yep, an HEI distributor. What I would do is to take the distributor cap off, leave the wires on it for now, (may want to mark the wire locations on the cap in-case you have to take them off) and then check the rotor, take it off and look underneath it for a burn, carbon mark in the center of it. If you see anything, then it needs to be replaced. Then there is a ignition control module screwed down with to screws, with wire plugins on each end of it. Take it out and bring it to a auto parts store to have it tested to see if it is bad. Also, look inside of the distributor cap for any cracks, see how the build-up is on each contact for the spark, scrape off any excessive build up, or replace the cap. If you plan on just putting on a new cap & rotor, then when you take the coil off of on top of the cap, take that in to have tested as well. Just be-careful of the wires too the coil. Check the center electrode while the coil is out. We'll start there.

Also tho, should investigate the fuel lines like 61LT suggested, most of the fuel line should be steel. Any long run of rubber fuel line hose would be suspect. Make sure and change out any fuel filters.