Blood vessels and other body lumens are expanded using an evertible braided prosthesis. The braided prosthesis is delivered to the blood vessel in a radially collapsed configuration. A leading edge of the braided prosthesis is then everted so that it expands as it is advanced through the blood vessel. Optionally, the prosthesis can be provided with a biologically active substance in order to inhibit hyperplasia or have other desired biological effects.