I'm wanting to up the displacement of my 350. The absolute max ci I want is 372. Easy, right? Wrong! The trick is, I'd like to do it without machining the block, unless that's impossible. What pistons (size and top shape i.e. dome, flat, dish), matching rings, and connecting rods should I use. Oh, and they need to be forged. Thanks for the help!!!  

why do you want 372, a cube limit? some calculations im missing? what?

If you get a 400 stroke crank with the regular large journal crankpins, it can be offset ground and small journal 2.0 rod bearings could be used from 283/327,this makes the engine ~367 cid with the standard bore (assuming when you mean not machining the block you mean not overboring as one of the things), also aftermarket cranks are available in 3&9/16 strokes that will displace 358's with stock 4 inch bores

no machining of the block might be impossible as in the extra stroke some clearancing of the buttom of the bores and pan rails may have to be done and depending on how wild the cam is also rod/cam interference becomes a problems, but this is nothing i can predict, it all will be told during the mockup

just as some advice, i dont believe chevy engines like domes, especially a OE style cylinder head as the spark plug is placed very low in the chamber and it doesnt take much dome to isolate areas of the chamber from the flame front

depending on what the engine will face will decide your choice on connecting rods, i dont believe H-beams are nessacary a lot of the time, maybe with a lot of Hp/ci on the bottle they might be though, also RPM range and usage will also determine rod length if you want to shoot for the 6.0 rods and get a little more trick for the extra upper RPM gain

i believe that engines that see a lot of miles will benefit from gapless second rings, i think a lot of common engines can benefit from gapless top rings, but these are so expensive i cant see getting them for a budget, mild street engine, but if the engine is seldom driven on the street sees frequent checks/rebuilds, i dont think you can beat a set of properly broken-in file fit moly rings

First you machine, then you buy parts to fit! (Well it's not quite that simple.) The only two ways to go from 350 to 372 is to bore the block (cylinders oversize) or stroke the crank (lengthen the distance from the main bearing to the rod bearing centers), or some combination of the two processes.

There are folks that build a 377 using a 350 crank, 3.48 inch stroke down from the 400's 3.76 inch stroke by putting it into a 400 block with a 4.155 bore. This requires a special thick backed main bearing inserts as the 350 crank's mains are .20 inch smaller in diameter than the 400. I guess doing this you could claim no block machining. But you don't have a 400 block to start with. You can also get to 377 by using a 400 crank in a stock 4 inch bore 350. In this case you turn the crank's main journals down .2 inch to the 350 bearing size. So you machined the crank but not the block.

Boring the 350 block an eigth inch over (.125) with a stock stroke crank would get you right on 372, but it's unlikely that anything short of a Rocket block or an aftermarket competition block could withstand that much bore and still keep coolant out of the cylinders. Besides, now you're machining the block.

The answer is there's no way to do this that doesn't require something get modified and or machined; and we ain't even got to fitting rods that miss all the other parts while their spinning on the crank.

Bogie

You might have your combos mixed up:

-  372ci is a standard 400 block (4.125") with a standard 350 crank (3.48"). 

-  377ci can be two different combos:  A 400 block punched +0.030" w/ a 350 crank.  Or a standard 350 block (4.001") with a standard 400 crank (3.75").

-  383ci is a 350 block punched +0.030" w/ a 400 crank.

The only way to get a 372ci from a 350 block would be to use a custom crank.  Example:  A +0.030" 350 block with a 3.65" crank.  Net net, you can't get to 372ci with the stock 350 crank without boring the block +1/8"... and that type of over-bore is not doable with a 350 block.

* Formula for cid = Bore x Bore x Stroke x 0.7854 x Number of Cylinders.