An atraumatic heart valve prosthesis includes a prosthetic valve coupled to an expandable anchoring structure including a outflow portion configured to taper inwardly in a distal direction towards a central axis of the prosthesis. By this configuration, the distal end of the anchoring structure imparts less force upon the vessel wall (e.g., the aortic tunica intima) during continued expansion and contraction of the heart. The expandable anchoring structure can be balloon expandable or self-expanding.