The envelope look on fondant cakes is pretty east to do, but you can also do the same thing with buttercream-covered cakes. Using square cakes, cut out four fondant triangles per tier. The base of each triangle should be the same length as the side of the tier plus two inches, and the height should be the height of the tier.
Apply the triangles to the corners of the cake by using more buttercream (or just wetting the back of the triangle if you're attaching it to a fondant cake. As long as the base of the triangle is the right length, the bottom edges should overlap by 1" at the base of the tier. If you want more overlap, just make the length of the triangle base longer.
This can be done with fondant or modelling chocolate. You might want to add a little tylose to the fondant if you're going to use that, since it will help it to keep its shape.