Flat kite. The oldest and most basic shape, it is often in the shape of a diamond or a rectangle. A flat kite needs a tail to supply drag and keep the kite pointed toward the sky. This can be made of cloth strips, tied end to end. A kite should begin with a tail at least seven times its diagonal length. The more wind, the longer the tail is needed.
Bowed kite. This kite is curved on its face to create an angle into the wind, which provides stability without a tail. A favorite bowed kite is the two-stick diamond-shape kite patented in 1891.
Box kite. This is made up of 3-D units whose sides are squares, rectangles or triangles. The units can be combined in countless ways. Invented in 1893, box kites require strong, steady wind.
Delta kite. Roughly triangular, most delta kites also have a flap of material, called a keel, which is perpendicular to the surface and attaches to the flying line. Delta kites (which led to the development of hang gliders) fly easily in light wind.
Flexible kite. This kite is sewed or taped together in a design that takes its shape from the wind. An example is the parafoil, which is similar to a parachute. It has no rigid frame.
Source: World Book Encyclopedia