The disclosure provides valve prostheses and methods of installation. One embodiment of the prosthesis has a generally tubular body adapted for placement proximate a mitral annulus. The tubular body has a generally tubular upper portion adapted to substantially reside in the left atrium above the mitral annulus. The generally tubular upper portion has a first circumferential wall that is outwardly biased to urge against cardiac tissue of the left atrium. The tubular body also includes a lower portion extending downwardly from the generally tubular upper portion, the lower portion being configured to substantially reside in the left ventricle below the mitral annulus. The lower portion of this embodiment can be defined by an generally circumferential wall that extends downwardly from the generally tubular upper portion. The generally circumferential wall has a first circumferential end and a second circumferential end, and defines a circumferential extent therebetween.