There are a variety of reasons to make crafts with cardboard -- it is a cheap, plentiful and flexible medium, well-suited to many kinds of projects. Whether you are constructing a model, an art project or a piece of furniture with cardboard, you may need to strengthen the cardboard so it can withstand the piece's intended use.
Things You'll Need
Wood glue or white glue
Shellac or varnish
Weights to hold down glued cardboard
Use good quality cardboard--this does not mean you need to buy it. Good, clean, used cardboard boxes can be acquired at many businesses and other establishments, free for the asking. Folds in cardboard compromise its strength, so try to use boxes whose sides are big enough for your purposes.
Use a tab and glue system for joints. To do this, when cutting out your pieces, cut an extra tab a few inches wide, depending on the size of the piece, on one side that is to be joined. Score the line with a box cutter between the tab and the rest of the piece. Fold backward on this joint. Cover the tab with glue and use it to attach the other piece. Generously apply duct tape on top of the seam to strengthen further.
Paint the entire outer and inner surface of your cardboard with glue, shellac or varnish to strengthen and even waterproof it to some extent. Or paint a sheet of cardboard with glue, lay another sheet on top, weigh it down and continue the process if desired. This will eventually give you a solid 3-D cube to work with. You can sculpt out of your cube as if it were rock, or use it as a solid base to build upon.
Use supports if your 2-D structures need extra strength. Duct tape any stiff, long objects to the inside or back of your wall or other structure. Try chopsticks, rulers, dowels or craft sticks, depending on the size of the structure.