Sometimes you don't know if you want to take the time and trouble of stretching and mounting a canvas, such as if you're pondering a series of small, quick paintings or want to try out an idea that's just in its infancy or a technique that's new to you. Or maybe you need to roll it up for shipping or travel right away or don't have a lot of storage room. Well, you can paint on unstretched canvas (please note that an "unstretched" canvas here does not mean "unprimed"), but you need to consider a few things before you uncap your tubes.
The same painting techniques apply whether you're working on unstretched or stretched canvas, whether it's acrylics or oils you're using. The challenge lies not so much in how you apply the paint but in getting the canvas to not curl at the edges or move or flop about too much as you work on it. There's also the risk of damaging the painting if you stretch it later.
You can tape, nail, or pin the piece of canvas to a wall, board, tabletop, or even the floor. Big clips on the edges of a drawing board work, too. Or, if the canvas is lying flat on the floor, apply some heavy objects to its corners, such as tubs of paint or a half-brick.
Heavier-weight canvas and larger unstretched pieces will straighten somewhat under their own weight if hung but not so much just lying on the floor without weighing them down, particularly if you allow yourself to stand on the work, as contemporary landscape artist Kurt Jackson does.
If you're used to moving a canvas around as you paint—for instance, turning it upside downit may work best to clip it onto a drawing board to retain this option. What you may also miss if you're accustomed to working on stretched canvas is the bounce of the surface. When nailed against a wall it'll be more rigid, like working on a board.
If the painting will be stretched later, remember to allow for part of the canvas going over the edge of the stretcher bars when finalizing the composition. There is a risk of paint buckling, cracking, and warping when stretching is done after the fact. You can also pull paint off the surface as you grip the canvas with your hands or pliers, and it's hard to get a painted canvas as tight as one that's been stretched ahead of time. If in doubt, practice on an unimportant painting or take it to a professional framer with experience in doing this.
Not stretching it is, of course, also an option. The painting could be displayed by attaching only the top to a wooden bar (a dowel, or even a solitary stretcher). If it's a small painting, it could be mounted in a box frame, as is done with watercolor paper. Larger paintings could be adhered to wood planks, foam board, or other rigid paneling.
If you prefer storing your paintings unmounted, you can stretch the canvas before painting, unmount to store it or travel with it, and then remount to display later. If you need to roll it up for travel, stretched or unstretched, place it face-down on archival paper prior to rolling it.