A shaped chimney liner is used for various reasons. Shaped chimney liners can be in square, oval or rectangle. All of these have their own components. A square chimney liner will have a square tee, top plate, and cap. This is all to make you installation easier.
Why would you ever use a shaped chimney liner? Basically it is used to maximize the space within the chimney flue. For example, if you have an appliance and the stove pipe is 8 inches, generally you will need an 8 inch liner. But if your current flue size is 8 x 13. Those are the outside dimensions, but the inside will be around 6 x 11 roughly. But there is no way to fit an 8 inch round liner down a 6 inch hole.
So instead of the time consuming work to remove the flues to make it possible for a round chimney liner you can ovalize it. The best would be to ovalize the liner to a slightly smaller size than the inside dimension. So in this case 5.5 would be good. That would make the liner 5.5 x 9.5. plenty small enough to fit inside an 8 x 13 flue. So instead of spending hours of labor removing the flues, you spend a few extra dollars on an oval chimney liner and get the job done in no time.
Another example may be when you need to install a chimney liner for a fireplace. For a fireplace you are concerned about the flow. Flow is the cubic inches of air flow traveling thru the chimney. So you need the proper size liner to have sufficient flow in your fireplace.
Chimney Liner Sizing Chart
Sometimes the size of the fireplace opening requires more square inches than a round liner can provide. So to maximize the square inches of the chimney liner, you can make it square, in a sense you are filling the corners of the flue with a chimney liner compared to leaving them empty with a round liner. Think of putting a round peg in a square hole or a square peg in a square hole. Obviously the square will fill the hole more, giving you more square inches for better flow.
One thing you must remember is that shaping a chimney liner makes it lose some of it flexibility. Obviously if it is square it will not make 45 degree bends now. But it still will be able to make it down a chimney that is built on a slight slant. An oval liner still has lots of its flexibility on it wider size. The wider flatter side will still be able to make it around sharp bends but the narrower side becomes a little stiffer.
Another word of caution is when you are installing an oval chimney liner be sure that it does not kink on you, or bend too sharply in the middle. You need to install it making a large rainbow. Make a large arc with the liner and like this you will avoid all damage to the liner. At least 2 people are required for a shaped liner installation.