No, according to the NCHFP and USDA, you'd have to can a seafood soup for 100 minutes, so it's quite a long processing time. 10 minutes vent time+100 minutes processing+10 minutes wait time after return to zero.

The usual soup restrictions apply regarding ingredients and proportions, i.e. no more than half solids and dairy would have to be added when reheated, not canned with the oysters.

Carol

Here is a link that might be useful: NCHFP Canning Soups

Since as Carol says, you really can't can oyster soup as such (no dairy products added which is 80% of it anyway) why not just can the oysters per the instructions for them - "Fill half-pint or pint jars with meat and hot water, leaving 1-inch headspace." and then turn them into oyster soup after opening? Much easier.

Dave

Here is a link that might be useful: NCHFP - Canning oysters