Generally speaking, the carrier will accept duffel bags, suitcases, plastic bins, banker boxes, and all sorts of different types of containers. Even though you can (although some carriers have refused duffel bags and other problematic containers), it is not recommended that you ship using any of these types of containers.
Always aim to package your goods within a cardboard box.
For one, all other types of containers have a high likely hood of losing their shipping label. Lost shipping label means lost package.
With duffel bags and suitcases, there is also a chance that straps or handles get stuck or pulled into the high speed conveyor belts. When that happens, there's a good chance your shipment will split open or the items within it damaged.
Here at Secureship, we're very cautious shippers. If you're not sure how to package your goods or don't have the necessary material to prepare your shipment, try bringing your items to a UPS store and getting them packaged (or any other packaging professional).