A system (30) for loading a replacement valve prosthesis (100) onto a minimally invasive delivery system, such as a delivery catheter (32). The system may include one or more frustoconical housings (34, 42) which define a tapered surface (60, 94). The prosthesis may be moved along the tapered surface to compress the prosthesis. Desirably, for compression of the valve portion (104) of the prosthesis, the prosthesis is moved along the tapered surface in a direction wherein the inlet end (106) of the valve leads an outlet end (108) of the valve. After compression, the prosthesis may be loaded into the sheath (44) of the delivery catheter. Methods of loading the replacement valve prosthesis are also disclosed.