If you are considering the option of building your own foam RC airplane, then you will want to weigh the options of which material to build it from. These two materials, EPS-Depron and EPP, are the most commonly used foams for just such a task.
EPS (expanded polystyrene), comes in several forms, depending on the application, however, Depron is the form used commonly for RC airplane fabrication. Depron is stiff and brittle, yet easily painted if using the correct type of paint. This foam is easy to cut, and moderately easy to sand to the desired contour. Standard Cyanoacrylate glue (CA or superglue) will dissolve this type of foam, as well as some spray adhesives and spray paints. There is no greater disappointment than to spend your valuable time, money, and effort building a beautiful model, bringing out the spray paint and watch all your craftsmanship dissolve into nothing but a pile of goo! So, take special care to select a friendly adhesive and paint. Low temperature hot glue works great, and water-based paints are preferred. Experienced models are most likely to select EPS-Depron to build an RC airplane from scratch because of its stiffness and ease of contouring.
EPP (expanded polypropylene) is soft and pliable; And because of it's softness is able to withstand moderate impacts. This foam is difficult to cut and near impossible to sand. Contouring can be accomplished, however, with a rasp tool. Cutting can be done with a very sharp knife, box cutter, or a hot wire cutter. Adhesives work fine on EPP including CA, low temperature hot glue, and many others. Painting onto EPP can be accomplished without worry of destruction by dissolving. Beginning RC pilots will be happier with their EPP construction because the RC airplane will be able to withstand crash after crash during the learning curve and still fly.
Construction of an RC airplane from either EPS-Depron or EPP is basically the same, with the exception of the slight differences in technique because of the material softness or brittleness. In both cases, you can use low temperature hot glue, a hot wire cutter, a jigsaw, and a box cutter. The main construction differences come in the areas of the aircraft that need extra support. The softness of EPP allows it to flex. Therefore, it is highly recommended that you add carbon rods in critical areas by cutting a groove into the material where you want the reinforcement, place the carbon rod in place, and fill in the groove with hot glue. Also, additional reinforcement of large areas can be accomplished using fiberglass mesh and epoxy, or by using duct tape. Control horns should be reinforced locally on both sides of the foam, and engine mounts should be doubly secured so as to not strictly sole on just glue by cross pinning the mount through the airplane body. Then the body of the foam plane can be painted, covered with colorized shrink wrap, tape stripes and stickers of your choice. Add electronics, control rods, and an engine, then let the excitation begin!