A prosthesis for locating at a branch region of a blood vessel. The prosthesis comprises a main conduit (10) having a tubular portion (11) with first and second ends (12,13), and at least one projecting portion (14,15,16) projecting from the first end of the tubular portion. One or more branch conduits (17,18) are connected to, and extend from the projecting portions or the tubular portion at a position adjacent the projecting portions. Portions of the prosthesis to which the branch conduits are attached may be more flexible and/or elastic than other portions of the prosthesis.