I have a buried system at 250 deg F with a 6" header and 3/4" branches
going up and out of the soil. I'm wondering how to model the 3/4" branches
as far as coding them as buried pipe with the same depth of the soil or possibly with an average depth. I'm wondering if the program has the capacity of analyzing vertical buried piping. In reality if the header pipe is moving horizontally with a large thermal movement the 3/4" branches will be resisted by a very large earth resistance, much more than the depth of the pipe. In fact they may all fail based on that type of analysis.

Anyone have any experience with this type of analysis?

This is a common situation in buried pipe where instruments, pig signallers etc need to be above the surface.

Model the branch with a offset if you wish. Then use the buried / unburied switch to turn on / off the soil resistance forces locally.

You may want to consider soft backfill around your branch, and increasing your branch size in the soil. 3/4" is incredibly small. The usual limit for a branch would be around 2" off a buried pipe. Soft backfill could be bagged polystyrene beads.