The invention is methods and devices which a surgeon may use to stabilize the beating heart during a surgical procedure on the heart. Pursuant to the invention, a stabilizing device is introduced through an opening in the chest and brought into contact with the beating heart. By contacting the heart with the device and by exerting a stabilizing force on the device, the motion of the heart caused by the contraction of the heart muscles is effectively eliminated such that the heart is stabilized and the site of the surgery moves only minimally if at all. Typically, in separate steps, the surgeon contacts the heart with the stabilizing means, assesses the degree of movement of the anastomosis site, and exerts a force on the stabilizing means such that the contraction of the beating heart causes orgy minimal excess motion at the surgery site.; By fixing the position of the stabilizing means in a configuration where the motion of the beating heart is effectively eliminated, the surgeon is able to stabilize the beating heart for the duration of the procedure. The stabilizing means may be attached to a rigid support or may be attached to a semi-rigid support which is rendered motionless mechanically, chemically, or by human intervention. In certain preferred embodiments, the stabilizing means is affixed to a semi-rigid support which is caused to become rigid, by any of a variety of techniques, such that the position of the stabilizing means becomes fixed by the support, and the heart remains substantially motionless for the duration of the procedure.