A prosthetic mitral valve assembly is disclosed. In certaindisclosed embodiments, the prosthetic mitral valve assembly has a flaredupper end and a tapered portion to fit the contours of the native mitralvalve. The prosthetic mitral valve assembly includes a stent or outersupport frame with a valve mounted therein. The assembly can be adapted toexpand radially outwardly and into contact with the native tissue to create apressure fit. The mitral valve assembly further includes tension membersbetween the leaflets of the valve assembly and a suitable location on theheart.