A mitral valve annulus reshaping device includes at least a portion that is formed of a biocompatible shape memory alloy SMA having a characteristic temperature, Af, that is preferably below body temperature. The device is constrained in an unstable martensite (UM) state while being introduced through a catheter that passes through the venous system and into the coronary sinus of the heart. The reshaping device is deployed adjacent to the mitral valve annulus of the heart as it is forced from the catheter. When released from the constraint of the catheter, the SMA of the device at least partially converts from the UM state to an austenitic state and attempts to change to a programmed shape that exerts a force on the adjacent tissue and modifies the shape of the annulus. The strain of the SMA can be varied when the device is within the coronary sinus.